
THE GENETICS OF SQUAREHEADEDNESS AND OF 

DENSITY IN WHEAT, AND THE RELATION 

OF THESE TO OTHER CHARACTERS 



SABKIS BOSHNAKIAN, M. S. in Agr. 



A Thesis Presented to the 

Faculty of the Gmduate School of Cornell University, March 1920, 

in partial fulfillment of the requirements for the 

Degree of Doctor of Philosophy 



Reprint of Memoir 53, (May 1922), Cornell University 



Agricultural Experiment Station 



MAY, 1922 MEMOIR 53 

CORNELL UNIVERSITY 
AGRICULTURAL EXPERIMENT STATION 



THE GENETICS OF SQUAREHEADEDNESS AND OF 

DENSITY IN WHEAT, AND THE RELATION 

OF THESE TO OTHER CHARACTERS 



SARKIS BOSHNAKIAN 



t 



ITHACA, NEW YORK 
PUBLISHED BY THE UNIVERSITY 






\^ 



^a- 



CONTENTS 

PAGE 

Physiological conditions affecting rachis internode length 802 

Determination of density and of squareheadedness 803 

Development of the whaat plant with reference to squareheadedness 804 

The mechanics of squareheadedness 806 

Effects of crossing on squareheadedness 807 

Effects of nutrition 809 

Summary 812 

The genetics of squareheadedness 813 

Inheritance of squareheadedness in crosses within the sativum group. . .. 814 
Relation of the degree of squareheadedness of the vulgare parent in 

vulgarc x squarehead crosses, to the squareheadedness of their progem- 824 

False dominance of squareheadedness 826 

Relation of width of culm to squareheadedness 827 

Inheritance of squareheadedness in spelt x sativum crosses 829 

Effect of the spelt factor on squarehe;idedness 831 

Inheritance of squareheadedness in specific crosses 833 

Summary 834 

The genetics of density 835 

Inheritance of density in crosses betw"een Triticutn compactum and other 

forms of the sativum group 836 

Inflence of the density of the lax parent in a lax x compactum cross on 

the density of succeeding generations 843 

Relation of density of F2 plants to that of their progeny 844 

Relation of density of dense and lax segregates of heterozygous F2 plants 845 
General consideration on the frequency distributions of compact x lax 

crosses 846 

The nature of density factors 854 

Factors producing squareheadedness as comprising one of the group of 

factors modifjnng degree of density 856 

Relation of squareheadedness to density in F2 -generation plants 858 

Relation of length of rachis to density in hybrid plants 865 

Relation of length of culm to rachis length and density 866 

Correlation between average internode length and length of sterile glumes 870 

Correlation between average internode length and length of kernels 871 

Relation of density of rachis to density of racliilla 872 

The factor for spelting acting as a modifier for the density factor 874 

The synthetic production of 7 riticum compactum 876 

Summary : 879 

Literature cited 881 



THE GENETICS OF SQUAREHEADEDNESS AND OF 

DENSITY IN WHEAT, AND THE RELATION 

OF THESE TO OTHER CHARACTERS 



THE GENETICS OF SQUAREHEADEDNESS AND OF 

DENSITY IN WHEAT, AND THE RELATION OF 

THESE To OTHER CHARACTERS' 

Sarkis Boshnakian- 

The niendelian inheritance of each of the more striking characters in 
wheat, such as beardedness, color, fehing, density, and so forth, has 
heen determined quaHtativel}- by various workers. Much remains to be 
done, however, if the genetics of these characters is to be analyzed from 
a quantitative point of view, as there are numerous lesser inherited varia- 
tions within their simple gross segregations. 

Practically all of these characters show certain degrees and types of 
interrelations with other characters. Some of thenv show complete or 
liartial linkage. Others, when analyzed quantitatively, appear to have 
been affected by one or another character but not necessarily linked with 
it, so that if one of these characters appears in an intense or a dilute 
form the others vary also in the same direction and more or less in the 
same degree. 

Besides the above-mentioned type of interrelation, in which the ap- 
pearance and the intensity of appearance of a group of characters are 
due to the presence or the absence of the same factor or factors, there is 
another type embracing a set of characters that appear as an indirect 
effect of the presence of another character. In a sense these characters 
are acquired, but they seem to be inherited simply because the causal 
character is inherited ; and whenever the latter is present it gradually 
causes the modification of the former characters during the lifetime of 
the individual. 

The subject of the inheritance of types of internode length presented 
in this paper has been treated from the following three viewp>oints : 
(i) the analyses of minor segregations within gross (3:1, i :2: i, or the 
like) segregations; (2) the determination of the interrelations of varied 

' Paper No. 93, Department of Plant Breeding, Cornell University, Ithaca, New York. 
Also presented to the Faculty of the Graduate School of Cornell University, March, 
1920, as a major thesis in partial fulfillment of the requirements for the degree of doctor 
of philosophy. 

-In cooperation with the Office of Cereal Investigations, United States Departmeni 
of Agriculture. 

801 



8o2 Sarkis Boshnakian 

characters; and (3) the determination of characters that were found 
to be the resultant of other characters. 

Since the characters studied were confined to those that were not 
distinctly contrasting in the usual niendelian sense but represented dif- 
ferent gradations on a scale between two extreme cjuantitative charac- 
ters, it was not possible to classify them into genetic classes or to express 
the results always- in terms of ratios. The analyses were made according 
to such biometrical methods as seemed best suited to bring out the direc- 
tions and tendencies of the variations. Factorial explanations, however, 
have been given wherever the tacts obtained warranted the formulation 
of such hypotheses. 

The material on which observations were made consisted, exclusive of 
interspecific crosses, of more than sixty F, progenies, fourteen of which 
were carried through the F3. To avoid duplications of similar results it 
is not considered necessary to present here the results of all the crosses, 
but sufficient data are given to serve as illustrations and to show the 
general trend of the various modes of inheritance. 

For many valuable suggestions and criticisms during the progress of 
this work the writer fully acknowledges his indebtedness to Professor 
H. H. Love, of the Department of Plant Breeding at Cornell University, 
under whose direction the studies were made. Most of the Fj and F3 
progenies studied were furnished by Dr. C. E. Leighty, of the United 
States Department of Agriculture. The writer wishes to express his 
appreciation of Dr. Leighty's generosity in supplying these and also 
carefully numbered hybrid progenies, which made possible the tracing 
of each back to the F, and parental material, all of which had been 
saved. Thanks are due also to the Office of Cereal Investigations, 
United States Department of Agriculture, through whose courtesy the 
writer was enabled to enjoy the field and laboratory facilities at the 
Arlington Experimental Grounds during the summers of 1916 and 1917. 

PHYSIOLOGICAL CONDITIONS AFFECTING RACHIS INTERNODE 

LENGTH 

Like many tiuantitative characters, density and squareheadedness are 
afi'ected to a greater or less extent by a number of environmental condi- 
tions which tend to change the normal course of development of the 
plant, thereby suppressing or accelerating the growth of certain of its 



Squareheadedness and Density in Wheat 803 

parts. A brief discussion of the effect of environmental factors on the 
production of these internode characters will serve to show to what 
extent nongenetic variations may take place. In the first part of this 
paper the main object is to explain the phenomena of density and square- 
headedness on a purely mechanical basis. 

DETERMINATION OF DENSITY AND OF SQUAREHEADEDNESS 

The terms density and squareheadedness are used in this paper to 
designate two different phenomena of rachis internode length. The 
differences between these two characters are discussed elsewhere (Bosh- 
nakian, 1917)', but they may be briefly redescribed here. 

Density is expressed in terms of average rachis internode length, 
which is found by dividing the length of the rachis by the number of 
rachis internodes. The average internode length, or density, of a head 
90 milliineters long with 20 rachis internodes, is thus 90 -^ 20, or 4.5 
millimeters. The average internode length in wheat varies from about 
1.3 to about 8 millimeters. In vulgar e wheat it usually does not extend 
beyond 5 millimeters. Density is comparative. 

The average internode length usually varies in dense wheats from 1.2 
to 2.5 millimeters, and in lax forms from 3 to 5-|- millimeters. There 
are intennediate gradations, but, in a general way, by dense or lax forms 
are meant, respectively, forms varying in density between the two ranges 
specified. Although the word club refers to a capitate type of head, 
following the present usage of this term it is here applied to dense wheats 
of the sativum group (that is, Tt-iticum conipactutn) whether capitate or 
not. 

Squareheadedness, on the other hand, refers to the ratio between the 
average internode length of the central third of the rachis and that of the 
terminal third. The density of the middle and upper thirds of the rachis 
is equal to the ratio of the number of internodes in these two sections 
of the rachis. The coefficient of squareheadedness is found by divid- 
ing the number of rachis internodes in the terminal third of the rachis by 
the number of internodes in the middle third. Thus, if the terminal 
third has 9.5 internodes and the central third has 5.6 internodes, the 
degree of squareheadedness is equal to 9.5 H- 5 .6, or i .69. The forms 

^Dates in parenthesis refer to Liieruiure Ciinl. page 881. 



S04 SaRKIS P.nSMNAKiAN 

that are usually called squarelieads have a coefficient of about 1.33 or 
more; and in this paper, by vulgare or non-squarehead forms are meant 
types with coefficients of less than i .33, and by squareheads, forms hav- 
ing coefficients of more than 1.33. This division is entirely arbitrary 
and is made for convenience. 

It is seen, then, that squareheadedness has no reference to density. 
Squareheads may be dense or lax. This divides the wheat tyjies into 
tlie following four classes with respect to their rachis internodes: non- 
squarehead, lax {Triticum vidyurc, Plate L,XVII, upper, 12) ; square- 
head, lax (Tr. capitattim, Plate LXVII, upper, 11) ; non-squarehead, club 
{Tr. compactuin, Plate LXV'II, lower, 13); squarehead, club (Tr. coin- 
pacto-capitaluiH Plate LXVII, upper, 9). These varietal names apply 
to the wheats of the sativum group only. 

According to these classifications, the semi-dense forms • having 
a squareheadedness of less than i . 33 are named seini-dense vulgare — not 
squareheads, a name too often applied for such forms, and perhaps with 
some justification as such semi-dense forms when well developed may 
appear square in cross section. 

Since the discussions in this paper center solely upon squareheadedness 
and density, it is necessary for the reader to bear in mind the sense in 

which these two terms are used. 

i 
df,ve;i,opment oi-' the wheat plant with reference 
TO squareheadedness 

The head of the wheat plant is found in an embryonic stage when the 
plant starts a new growth after a short or a long period of rest. When 
the head is about 10 millimeters long it is covered with concentric rings 
of sheaths, each sheath being attached to the culm at its respective node. 
The different parts of the plant do not all grow at the same rate. 

When the spike is about 15 millimeters long, the enveloping sheaths 
and blades are fairly well developed, but the culm internodes are only 
a few millimeters in length, the terminal ones being the shortest. After 
the sheaths have gone through their chief period of growth, the develop- 
ment of the internodes is accelerated. During this period the head also 
begins to develop. From this time on, the increase in the height of the 



Mf.moir S3 



Pj.atf. I.Wll 




W- 0'^ W'4 A"^ 



1+ ■^ly 



\ 



VARIOI'S FORMS OF GROWTH 

Upper: 1, Aegilops ovala: 2, Fl {Aegilops x Silver Club); 3, Silver Club. 4, White Spell; 5. Dale Gloria; 6 lo 12, F^' 
types (Whire Spelt x Dale Gloria, series 13255a) — 6. homozygous lax spelt; 7, heterozygous dense spelt; 8. 
homozygous dense itpell; 9, homozygous dense sativum (club); 10. heterozygous dense sativum; 11, homozygous 
lax sativum., squarehead; 12, homozygous lax sativum., vulgare 

Lower: Dense forms of different species: 1, durum: 2 and 3. rapitarc and den^e harley heads (lateral florets of 2 re- 
moved); 4. capitate sativum: 5, dense -ipelt; ti, den^e potontcnm: 7 and ft. rliib wheals; 9, titrf^idum: 10, club; 
11 and 12. capitate dicoccums; 13. club pyramidal; 14. capitate spelt; 15, dense po^tinirum; 16, club 



Memoir 53 



Plate LXVIII 




f' r 1 
"I 




VARIOUS FORMS OF GROWTH 

I'pper: 1 lo 5, 6 to 10. Heads of two hybrid plants showing lack of harmony of growth characters. 11 and 12, Heads 
of spelts eubjecled to longitudinal pressure; zigzagging of internodes produced instead of Hqiiareheadedneas 

Lower; 1 to 4, 5 lo 8, Heads of two plants showing vaiialiona in density on same plant; plants grown in greeDliouse; 
long spikes headed out about four weeks earlier than dense epikes 



SqUAREHEADEDNESS" AND DENSITY IN WlIEAT 8oS 

plant is due primarily to the increasing length of each culm internode. 
During the first period of the development of the culm, the basal inter- 
nodes, except a few near tlie ground, begin to develop, and successive 
internodes undergo their chief period of growth as the growth of the 
internode below is beginning to decline. The terminal section of the 
culm, which carries the spike, during its development has to push the 
spike up all along the length of the terminal sheath, which envelops the 
head in such a way that occasionally, and especially among plants of 
hybrid origin, the culm cannot exert sufficient pressure to unfold the 
.-heath. In such cases the spike fails to head out; or, if it finally does 
head out, the head appears in an abnormal condition and the tip spikelets 
very often remain undeveloped (Plate LX\'III, upper, i to lo). 

The factors that seem to produce a strain on the terminal culm inter- 
node during its growth are the following: the rapid growth of the culm; 
the spread, width, shape, and texture of the spikelets; the stiffness of the 
enveloping sheath and its resistance to unfolding. 

It seems that as the rate of growth of the tenninal culm increases, the 
movement of the spike through the sheath should encounter a greater de- 
gree of resistance in an opposite direction. 

The spread of the spikelets is probably one of the most important 
factors. The glumes of the spikelets are pointed upward and outward. 
This in itself tends to increase resistance. If the contact of the glumes 
with the sheath increases their spread, the resistance will in(iiease many 
fold. In species such as the spelt or the emmer, in which the spikes are 
very narrow and the spikelets are very close to the rachis, the resistance 
is decidedly decreased because the spikelets themselves assume a wedge 
shape, the glumes being drawn together tightly ; and also because the 
spikelets, lying flat against the rachis, are not likely to spread out. 

The third factor, which is not so important as the other two, is the 
texture of the sheath and its habit of development. The sheath that 
normally unfolds at the proper time, or is easily unfolded by the move- 
ment of the spike, sometimes fails to open completely or opens under 
difficulty. Sheaths of this type produce a considerable longitudinal pres- 
sure on the culm. 



So6 Sarkis Boshnakian 

THE MECHANICS OF SQUAREHEADEDNESS 

In order to understand the mechanics of the production of squarehead- 
edness, it is necessary to know the effect that is produced by pressure 
along the cuhii axis. The presence of longitudinal pressure is evident 
from the undulations of the culms often observed in square or dense 
forms (Plate LXVII, lower, 9 and 16.) The part of the spike that most 
reacts to the effect of pressure is the terminal part, because it is directly 
in contact with the sheath. The pressure produces a compressing effect, 
and this in turn checks the development of the terminal part of the head, 
especially the development of the rachis internodes, and produces the 
eft'ect known as squareheadedness. 

This character of squareheadedness is mainly evidenced by the gradual 
shortening of the terminal rachis internodes (Plate LXVII, lower, 4, 11, 
and 12). But there are also other characters which accompany this short- 
ening of the internodes and which are the direct or indirect results of the 
same cause. One of the most prominent of these is the so-called clubbing, 
or capitate form, produced by the spreading of the spikelets away from 
the rachis in those regions of the head where the internodes are short. 
Because of the pressure exerted, the normal elongation of the internodes 
is inhibited but the spikelets in most cases continue to develop. Since 
the space between the spikelets is not sufficient, they are forced mechani- 
cally to spread out to make more room for development. This process 
is on the principle of the isosceles trapezoid, in which, the base being 
constant, the distance between the sides increases as the latter take a 
position toward a right angle with the base. In the plant the rachis 
internode is represented by the base, and the axes of the spikelets by the 
sides, of the trapezoid. 

In squareheads the spikelets of only the upper part of the spike (ex- 
cept the terminal two or three spikelets) thus diverge. In most coin- 
pactum forms all spikelets diverge as a result of the shortness of all the 
internodes. This is seen on comparing the divergence of spikelets of 
dense heads 5 and 9, in Plate LXVII (upper), with that of lax heads 2, 
4, and 6. In wheat, as well as in barley, the opposite condition exists 
also in some cases ; that is, the shortening of the internodes does not occur 
near the upper part, but near the basal region. In such cases the ear, in- 



Squareheadedness and Density in Wheat 807 

stead of being capitate in form, assumes a pyramidal or conical form, as 
shown by heads 13, Plate LXVII (lower), and 8, Plate LXVII (upper). 

Another phenomenon of squareheadedness is the drawing of the ter- 
minal spikelets toward one side so that when the head is viewed along 
one of the directions of the plane of symmetry, which separates the 
spikelets of one side from those of the other, the rachis appears exposed 
(Plate LXVII, upper, 11). Viewed from the opposite side the rachis is 
covered by glumes and awns which are outdrawn and gathered in that 
direction. With the receding of the glumes the part of the side where 
the rachis is exposed appears flat (Plate LXVII, upper, 11), and to a 
person not viewing the head from the opposite side also it gives the im- 
pression that the spike is square in cross section. This impression, which 
has been left on the popular mind, has given to this form the name 
squarehead. 

The character of squareheadedness is not confined to the whea: known 
by this name but may appear also in the dense forms known as club 
wheats {Triiicum com pactum). The total shortening of rachis internodes 
in these forms is primarily due to the presence of a genetic factor which 
produces also a general shortening of many parts of the plant. But in 
most forms a certain degree of squareheadedness may be found. This 
may be inherent — that is, transmissible — or it may have been produced 
mechanically. When the spikelets spread out as a result of the short- 
ness of the internodes, as described above, the increased width of the head 
and the projections of the tips of the glumes are likely to offer consider- 
able resistance, thus producing squareheadedness in the manner already 
explained. 

EFFECTS OF CROSSING ON SQUAREHEADEDNESS 

Squareheadedness, and shortening of all the rachis internodes, are 
two ditiferent phenomena. As shown in the preceding discussion, square- 
headedness is a postnatal character, as it were, being dependent on the 
combined effect of certain vegetative growth characters. Density of the 
compactiim wheats, on the other hand, is predetermined and is due to 
the presence of one or more genetic factors which cause dwarfing of a 
number of plant parts, including incidentally the shortening of all rachis 
internodes. 

Squareheadedness is dependent on a certain balance of the rate of 



8o8 Sarkis Boshnakian 



b 



rowth of the parts concerned. An unfavorable balance produced 
through hybridization may result in certain hereditary anomalies. A 
few such forms are shown in Plate LXVIII (upper). Heads i to 5 were 
produced on a single F, plant derived from a cross between a durum and 
a common wheat. In these cases the curling of the awns all along the 
length of the heads shows that the latter were partly prevented from 
moving up the sheaths by the tightenmg of the sheaths. The illustrations 
show also the rudimentary condition of the terminal 5 to 7 spikelets, 
which represent the region whose growth was checked altogether by 
being subjected to pressure. 

Heads 6 to 10 in the same plate represent another condition of lack 
of harmony of growth iietween different parts of the plant. The spiral 
ionn of the awns of head 7 shows that this head was forced to make a 
corkscrew movement while making its way up the sheath. Heads 8 and 
10 show the failure of the sheath to open at the proper time. Heads 
6 and 9 represent heads that were finally released. 

Heads 11 and 12 represent a single spelt plant whose sheaths were 
evidently wrapped too tightly around the heads. The pressure which the 
tight sheath exerted on the head by the growth of the culm produced a 
zigzagging of the rachis. The internodes of the spelts, being compara- 
tively stifif, are not so likely to remain short as a result of pressure. 

These two spelt heads are interesting because they show the relative 
tendency of the different internodes to be affected by pressure. The 
basal internodes are thick and are very slightly affected by the induced 
zigzagging eft'ect. Each successive internode is weaker than the one 
below, and more and more likely to show the effect of pressure. The 
conditions to which these heads were subjected are identical with those 
to which squareheads of sativum or other soft-glumed species are sub- 
jected, but the effect is somewhat different because of the differences of 
texture and ear form of the spelt as compared with those of some other 
forms. 

These cases show that there are a number of growth characters to 
which the production of squareheadedness is due, and that the factors 
producing these characters seem to segregate and recombine like any 
other factors. H the combination is such as will produce a pressure of 



Squaeeheadedness and Density in Wheat 



809 



the head in a certain rate and intensity, various degrees of squareliead- 
edness may result. If the head encounters httle or ho presstu"e the in- 
temodes may be more or less uniform, and if the growth of parts is 
unbalanced certain abnormalities of the spike may result. 

Since a number of morphological factors are concerned in the pro- 
duction of squareheadedness, logically it would be expected, and experi- 
mentally it would be found, that the segregates of a cross between a 
squarehead and a non-squarehead do not appear in a definite ratio but 
give a distribution approaching the normal curve of error. 

EFFECTS OF NUTRITION 

In one of the preliminary experiments to determine the effect of nu- 
trition under field conditions, seeds from a pure variety of a squarehead 
were grown at varying distances. In one case the seeds were drilled 
rather closely; in the second case they were planted 7.5 centimeters 
apart; in the third case they were planted 15 centimeters apart. The 
frequency distribution of squareheadedness of these three sets of plant- 
ings is given in table I. The set that was drilled in had a mean degree 
of squareheadedness of 1.325 dz 0.012; the seeds planted 7.5 centimeters 

TABLE 1. V.\Ri.\TioNs OF Squareheadedness in Plants Grown at V.^rying 

Distances 
(Variety, Giant Squarehead) 



Seeds drilled 

Seeds planted 7.5 cm. apart 
Seeds plgntt-d 1.5 cm. apart 



Siluareheadedness 



1,00 I-IO 1.20 1.30 I 40il 3011 bO 1,70 1 80 1,90 2.00 2,10 2,20 



14 18 25 

6 



3 2 



Number 

of 
plants 



94 1 32o±,012 

42 1 fl7S± 025 

II I 1 2.M± 027 



apart gave a higher mean, 1.678 dz 0.025; 3"^ those planted 15 centi- 
meters apart gave a mean of but 1.254 ± 0.027. 

The plants from the drilled rows made a fair growth but were inferior 
to those of the second set. The plants of the third set were mostly win- 
terkilled, and such as survived had a poor stand with heads of varying 
length and degrees of development. The poor condition of the last- 
named was due to the wide distances between the plants, which made 
them unable to protect themselves from winter conditions. In the case 
of the other sets there was enough foliage developed during the fall 
for winter protection. 



8io Sarkis Boshnakian 

Disregarding the third set, it is apparent that the high degree of square- 
headedness of the second set was due to the greater feeding allotted 
to these plants ; for there was also a corresponding general development. 

Another experiment was made with potted plants growing under 
greenhouse conditions. It consisted of four sets of nine pots. One set 
was grown m a cool house, the second under moderate greenhouse con- 
ditions, the third in a damp chamber, and the fourth in a rather warm 
place. Each set consisted of triplicate pots containing, respectively, 
soils of a very poor sandy mixture, of fair fertility, and of higher fer- 
tility. 

In the sets grown in cool and moderate temperature conditions, the 
pots containing poor soil produced heads of a low degree of squarehead- 
edness, while the heads of plants grown in moderately fertile soils 
showed a higher degree of squareheadedness.* 

There is no question that in these cases the high degree of squarehead- 
edness was produced by the fertility of the soil. That fertility in- 
creases squareheadedness has been noted by Edler (1903), Preul (1908), 
Ohlmer (1908), and Meyer (1909). Aleyer found in addition that ni- 
trogen was the causative factor, as neither calcium, potassium, nor 
phosphorus, alone or in combination, had any noticeable effect on the 
production of this character. 

It is not so difficult to explain how high fertility increases square- 
headedness, in the light of the causes of squareheadedness given in the 
preceding discussions. If rapid growth of the culm subjects the head 
to higher pressure, the spike takes the squarehead form. By increasing 
the nitrogen content of the soil, the rate of growth of the culm is acceler- 
"atcd and the tissues of the parts of the head are softened. The first 
of these conditions increases the pressure to which the head is subjected, 
and the second renders the head more sensitive to the effect of pressure. 
In the absence of sufficient nitrogenous food, the rate of growth is re- 
tarded and the parts of the head become fibrous. Due to the first con- 
dition suflirient pressure is not developed, and with the hardening of the 
tissues the spike offers a greater resistance to whatever pressure niay be 
developed. 

*The sets grown in the damp cliamher and in the warm place did not do well. 



Squareheadedness and Density in Wheat 



Sii 



The effect of the rate of growth on squareheadedness maj' be deter- 
mined also by ascertaining the degree of squareheadedness of the leading 
culm and of those that develop later. Practically in every case the 
leader, which is by far the most vigorously growing culm, has a higher 
degree of squareheadedness than the others. Often the smaller culms 
of squarehead plants will have z'ldgare-Vike: heads. 

In cases in which squareheading is increased by the rapid growth of 
the culm, the plants having longer spikes are more squareheaded than 
those with shorter spikes. The relative degree of squareheadedness of 
short and of long spikes of the same plant is shown in table 2. From 
four to six well-developed heads w^ere measured from each plant in 
connection with another experiment. Here the shortest and the longest 
of these, respectively, are shown. Out of twelve cases taken at random 
there was but one case in which the short head had a higher degree of 
squareheadedness. The average of the summation of the differences 



was o. 



0.021 in favor of the long heads. 



TABLE 2. Differences in Degree of Squareheadedness of Long and of Short 
Heads of the Same Plant 



Short heads 


Long heads 


Length (centimeters) 


Squareheadedness 


Length (centimeters) 


Squareheadedness 


Difference in 
squareheadedness 


10 


1.23 


13.5 


1 47 


-i-0.24 


11,6 


1.41 


13.2 


1.51 


+0.10 


104 


1 50 


13.8 


1.50 


00 


10 3 


1.24 


12 


1.51 


+0.27 


10.7 


1.21 


14 


1.37 


+0.15 


10 5 


1 24 


13.6 


1.48 


+0 24 


8.0 


1 39 


10.5 


1.60 


+0 21 


7.6 


1.31 


10 


1.65 


+0.34 


8 7 


1.51 


10.1 


1.65 


+0.14 


8.4 


1 33 


11.2 


1.57 


+0.24 


8 3 


1 39 


12 5 


1.58 


+0.19 


7 9 


1 29 


10 3 


1 17 


-0 12 



Mean and average error 



12 0± 40 



1 .50± 026 



+n 17± 021 



When vigor is induced by soil fertility, the plants with longer heads 
will be more squareheaded than the others; and when vigor is induced 
by crossing certain zndgarc forms, the long heads of each plant will be 
found to be more of a squareheaded type. The increase of squarehead- 
edness of the Fj plants, as shown later, will serve as exaanples. 

If, on the other hand, squareheadedness is caused, not so much by the 



8i2 Sarkts Boshnakian 

vigorous development of the culm, but by the failure of the sheath to 
unfold at the proper time, then the plants that are more squareheaded 
will be found to have shorter heads that the non-squarehead forms. 
Figures illustrating this type of squareheadedness are given in connection 
with the discussion of that subject. 

Before concluding the discussion of the effects of nutrition, it may 
be well to make a few remarks regarding its effect on the density of the 
cotnpactum form. As already mentioned, the density of this form is 
not the result of pressure. But by increasing the fertility of the soil 
it is possible to change markedl} the degree of density. Four heads 
from each of two coiupactniii plants are shown in Plate LXVIII (lower). 
These two plants were grown in 4-inch pots in a greenhouse. The soil 
was highly fertilized. The heads tirst developed (2, 4, and 5) were 
almost like vulgare, but as the season advanced, and more spikes began 
to head out, the heads became more and more dense. There was an 
interval of about four weeks between the time of heading-out of the 
first and of the last head. When the last spike headed out, the first one 
was almost ripe — that is to say, the nutrients in the plant or those in the 
soil were already used up; hence the spikes heading out later obtained 
very little food. From the difference in thickness of the culms of dense 
and lax heads an idea may be formed of the relative amount of nourish- 
ment obtained by the different heads. 

This experiment was conducted under abnormal environmental con- 
ditions, and it is not likely that variations as great as these will be 
found on plants growing under field conditions. But it points out the 
fact that increased fertility in the soil tends to increase the length of the 
rachis internodes. 

SUMMARY 

The wheat plant during its development undergoes two more or less 
distinct periods of growth. In the first period the sheaths and the 
blades develop. In the second period the rate of growth of the sheaths 
diminishes and the culms begin to develop, and during this period 
the spike carried at the end of the terminal culm internode is pushed 
up through the enveloping sheath. 

Squareheadedness is the combination of a number of characters which 



Squarehe.m^edne^s and Density in Wheat 813 

are produced by the shortening of the terminal rachis internodes. It is 
expressed by the coefficient found by dividing the number of internodes 
in the terminal third of the rachis by the number of internodes in the 
central third. 

Density is the shortening of all the rachis internodes. It is determined 
by dividing the length of th.e rachis in millimeters by the nunaher of 
internodes. 

There are numerous gradations of squareheadedness and of density. 

Squareheadedness is the result of pressure developed by differential 
growth of culm and sheath. 

Rapid growth of the culm, failure of the sheath to unfcld, and ears 
with soft-spreading glumes, tend to increase squareheadedness. 

Any factor, genetic or environmental, which affects principally the 
development of the above-named characters, will affect the degree of 
squareheadedness. 

Fertilit}- of the soil or access of the root system to sufficient available 
nitrogenous matter increases squareheadedness. 

Density is purely an inherited character, but favorable growth con- 
ditions may somewhat increase average internode length. Under ab- 
normally favorable or unfavorable conditions, the increase or the de- 
crease of densitv even on the same plant may be considerable. 

THE GENETICS OF SQUAREHEADEDNESS 

Investigations on the genetics of scjuareheadedness have given many 
confusing results, chiefly because no definite standards have been used 
for measuring this character. There are many instances in which this 
word has been used for designating a moderate degree of density. 

One of the earliest studies of the subject was made by Rimpau (1891), 
who crossed lax vidgare types with lax and moderately dense square- 
heads. The Fj hybrids were intermediate and the types of the F, 
populations varied within respective parental ranges. 

Von Riimker (1909) obtained from squarehead x vulgare crosses, 
Fj populations, some of which yielded more and others fewer square- 
heads. The squareheads varied also in degree. 

Nilsson-Ehle (1911) found the vulgare type to be dominant over the 



814 



Sakkis Boshnakian 



squarehead form. The ratio of vttlgare to squarehead was between 
3:1 and 15:1. 

Further work" has been done, but because of the different meanings 
given to the word squarehead it is not possible to compare the resuhs 
with those that are here presented. 

INHERITANCE OF SQUAREHEADEDNESS IN CROSSES WITHIN THE 
SATIVUM GROUP 

Squareheadedness is a quantitative character. Crosses in which it 
is involved do not show a clear-cut segregation into mendelian classes 
and ratios. Physiological experiments have shown that the character 
is the result of the interaction of a number of growth factors, certain 
combinations of which cause the compacting of the terminal part of 
the spike. The character is very variable, for any environmental con- 
dition that affects these growth factors in one way or the other indirectly 
increases or decreases the degree of compactness of the terminal part 
of the rachis. 

Before considering tlie inheritance of the character in squarehead x 
non-squarehead crosses, it may be well to illustrate the mode of inheri- 



TABLE 3. Degree of Squareheadedness in Vui.gare 


X 


VULGARE 


Crosses 




Gener- 
ation 


Degree of squareheadedness 


Mean 


Number 
ot 













g 


s 





»c 


° 


^ 





10 





10 


s 


S 


§ 


S 


plantB 


Parent plants 

Mealy 

Jones Longberry 

Pride of Genesee. 

Dawson Golden Chaff.. , 
Crosses 
13158a Mealy 
X Jones Longberry. . . . 
13158a Mealy 
X Jones Longberry. . . 
13178a Jones Longberry 

X Mealv. 

13178a Jones Longberry 


Fi 
F2 
Fi 
F2 
Fi 
F2 
Fi 
F2 


'2 

1 

1 




1 
■3 

6 

2 
3 
3 


2 
1 
4 
6 

7 
3 

13 

1 
_25 


6 
2 
2 
2 

13 

8 

17 
1 
14 


6 
4 

14 

9 

15 

3 

_9 


7 
3 
6 

9 

5 

17 

2 

_6 


4 
2 

1 

5 

6 

.. 
10 

_6 


4 
1 
1 

6 

1 
4 

4 

2 


1 

1 

3 
4 

9 

4 

_i_ 


1 

1 

1 

2 
1 
2 

_2 


1 
3 


1 

1 
2 


2 


1 

■■ 


2 


1 


1.14 
1 12 
1.08 

98 

1.35 
1.12 
1.50 
1.17 
1.42 
1.11 
1.09 

1 06 


28 
15 
23 
17 

6 
61 

6 
55 


13179a Jones Longberry 


3 


13179a Jones Longberry 


90 


13177a Dawson Golden 
Chaff X Pride of Genesee 
13177a Dawson Golden 
Chaff X Pride of Genesee 


7 
70 



Sqcareheadedness and Density in Wheat 



Si 5 



tance of squareheadedness when either the squareheads or the. vulgare 
type (non-squareheads) are crossed among themselves. 

The degree of squareheadedness in Fi and F„ generations of vulgare 
X vulgare crosses is shown in table 3. The first three crosses here (series 
13158a, 13178a, and 131793) are between Mealy and Jones Longberry, 
both of which have practically the same degree of squareheadedness, i . 14 
and 1 . 12, respectively. The mean degree of squareheadedness of the 
F; generation fluctuated around the means of their parental forms, being, 
respectively, 1.12, 1.17, and i.ii. 

The fourth cross, 13177a, was made between plants of lower coeffi- 
cient; that of Pride of Genesee was 1.08 and that of Dawson Golden 
Chaff was 0.98. The F, generation from this cross were all non-square- 
heads and had a mean squareheadedness of i .06, these also somewhat ap- 
proaching the average of their parents. 

The degree of squareheadedness in crosses between squareheads 
is shown in table "4. The F.. of the first cross, 13201a, has a range with- 

TABLE 4. Decree of Squareheadedness iw Squarehead x Squarehead Crosses 





Gener- 
ation 


Degree of squareheadedness 


Mean 


Xumber 
of 





1 


W3 


2 


4 
_2 




2 
4 



'2 

11 

_7 


"2 

8 

1 

_4 


1 
2 

12 

7 


2 
'2 

7 
fi 


'3 

4 

10 
_4 


3 
2 

2 

1 

_5 


CO 
1 

2 

_7 




3 
5 
1 

6 
1 
3 


•0 

2 
4 

1 
1 

_2 


2 
4 

2 
_2 


.0 

1 

1 

1 


2 
4 

2 


i 

1 


S 
■3 


2 
1 




1 


plants 


Parent plants 
New Soules 


Fi 
F2 
Fi 
F2 


1.71 
1.77 
1.49 

1.87 
1.46 
1.55 
I.IJS 


15 




33 


Jones Mammoth Amber 

Crosses 

13201a New Soules x Giant 

Squarehead 

13201a New Soules x Giant 

Squarehead 

13203a Jones Mammoth Amber 

X Giant Squarehead 
132fl3a Jones Mammoth Amber 

X Giant Squarehead 


15 

5 

72 
3 

52 



in the squarehead classes with a mean of 1.46. Compared with the 
averages of the parental forms — Xew Soules, 1.71, and Giant Square- 
head, 1.77 — the mean of the F„ is lower. The second cross, 13203a, 
has an F^ mean squareheadedness within the means of the parents. 

There are two points of interest in connection with these two sets of 
crosses : first, as a rule, when vulgare forms are crossed among them- 
.>elves or squareheads are crossed among themselves, the Fn generation 



8i6 Sarkis Boshnakian 

TABLE 5. Decree of Squareheadedness in Squarehead x Vulgare Crosses 





Gener- 
ation 


Degree of squareheadedness 


Mean 


Number 




o 
1 

Nc 

N 


o 

1 

t r 
1 

nt T 


o 

1 
ceo 

1 


o 

1 

1 

1 

2 
4 
1 

rde 
1 


§ 
o 

1 
1 
3 

3 

2 
1 

8 
2 

d 
I 

1 

3 
'd 


§ 

11 

3 

6 
2 
14 
8 

I 
i 

3 
4 
i 
6 

4 

3 

4 


6 
6 
3 
5 
2 
2 
6 

11 
3 
4 

'4 
6 

13 

13 

2 
S 

7 
'4 
'3 

io 

'4 

'2 
w 
4 



s 

2 
3 

4 
6 
2 

11 

3 
6 
11 
1 

'9 
11 

'3 
16 

5 
6 
6 
'4 

is 

6 
14 
_3 


'8 
7 
2 
5 
6 
3 
2 

17 
5 
6 
9 
7 
8 
4 

■3 

io 

7 
'2 

9 
'9 
'5 

8 

14 

10 


S 
4 

2 
1 
2 
I 

21 
7 
9 
'7 
11 
11 
8 

6 
6 

8 
9 

io 

S 
13 

14 

■9 


18 

18 

1 
4 

11 

11 

6 

'7 

io 
i3 

10 

8 

ii 

13 

■9 

11 

'7 
\2 




2 
1 
1 

1 

17 
9 
8 
9 

11 

S 

1 
7 

8 
'5 

7 
6 
'4 
■3 

ii 
12 

's 



2 

'2 
1 

1 

4 

2 

6 

1 

8 

8 
12 

7 
8 

i4 

6 

'7 
'7 

'4 

2 

7 

10 

7 
4 




6 
2 

8 

3 
9 
'7 
9 

4 

1 
3 

12 
'7 

3 

i2 

'3 

'3 

'7 

2 
6 

1 
3 

_5 


in 

1 
3 
2 

5 

1 
5 

5 

2 

11 

1 

4 

6 

10 

1 
2 

6 

4 

3 

2 

16 

'3 

1 
4 

5 


s 

2 
4 

2 

■ 

3 

1 

4 

2 
2 

2 

1 

12 

1 
3 

1 
I 

9 
2 

4 
2 

i 

■2 

1 
5 

1 

■3 
2 


S 

3 
4 

4 

1 
2 

5 

3 
8 

6 

1 
1 

■7 

1 
1 

2 


g 

1 
3 
1 

2 

I 
1 

4 

1 
6 

1 
5 

1 
2 

1 
1 

'7 
1 

3 

2 
1 


g 

1 

1 

■ 

4 

2 

i 

1 

2 
2 

2 

2 

'4 

1 

2 
I 

1 

1 

1 

1 

J 


5 
3 
2 

1 
3 

1 

2 
1 

1 
1 


4 
2 
1 

1 

i 
■3 

'4 

1 
2 

1 
1 

1 


^ 

4 
2 

1 

i 

1 
2 

1 

1 

2 
i 


1 
1 
1 

' i 

2 
1 

1 



as 

4 
2 

1 
1 

1 


1 

1 
1 





3 


° 
2 




1 


of 
pLints 


Parent plants 
Giant Squarehead.. . 

New Soules 

Extra Early Windsor 
Jones Mammoth 


Fi 
Fa 

F. 
Fa 

Fi 

F2 

Fi 
Fa 

F, 

F2 

Fi 
Fa 

Fi 
Fa 

Fi 
Fa 

Fi 

Fa 

Fi 

Fa 

Fi 
Fa 

Fi 
Fa 

Fi 
Fa 

F, 
Fa 

Fi 
Fa 

Fi 
Fa 

Fi 

Fa 


1.77 
1 71 
1 57 

1 49 
1 15 
1 14 
1 04 
1 12 
1 08 
1 12 
1 08 

1 35 
1 24 

1 41 
1,31 

1 40 
1 33 

1.62 
1.29 

1.62 
1 36 

1 51 
1 21 

1 47 
1 22 

1 77 
1 40 

1 55 
1.22 

1 28 

1.68 
1.30 

1.32 
1.24 

1,75 
1.25 

1.40 
1.25 

1 46 

1 24 

1 42 
1 22 

1,27 


33 
15 
24 

15 


Minnesota 169 

Mealy 

Fultz 

FultzrvMedit 

Pride of Genesee 

Jones Lungberry 

Rural New Yorker, - 
Crosses 

13131a Giant Square- 
head X Minn. 169 . 
Ditto 

13150a Minn. 169 
X Giant Squarehead 
Ditto 

ISlotia Minn. 169 
X Giant iSquarehead 
Ditto 

13134a Giant Square- 
head X Mealy 

Ditto 

13135a Giant Square- 
head X Mealy 

Ditto 

13137a GiantSquare- 

head x Fultz 

Ditto 

13138a Fultz x Giant 

Squarehead 

Ditto 

13140a Giant Square- 
head X Fultzo- 

Mediterranean 

Ditto 

13141a Giant Sq. 
X Pride of Genesee . 
Ditto 

13200a Pride of Gen- 
esee X Giant Square- 


41 
28 
13 
13 
23 
15 
12 

1 
135 

4 

75 

4 

74 

2 
95 

5 
121 

3 
111 

5 
89 

2 
101 

3 
71 


Ditto 


76 

4 

74 

6 
6.-1 

1 

76 

3 

85 

4 

73 

2 
95 


13202a Jones Long- 
berry X Giant Sq.. . 
Ditto 

13194a Pride of Gen- 
esee X New Soules. 
Ditto 

13144a New Soules 
X Pride of Genesee. . 
Ditto 

13176a New Soules 
X Rural New Yorker 
Ditto 


13196a Pride of Gen- 
esee X Extra Early 
Windsor 


13193a Junes Mam- 
moth Amber x 

Meaty 

Ditto 

13143a Extra Early 
Windsor x Pride of 
Genesee . . . 


Ditto 




_ 


_ 


_ 


_ 


J_ 


64 



Squareiieadedne^s and Density in Wheat 817 

consists of practically only vulgarc or only squareheads, respectively ; 
secondly, the mean of the F, generation approaches the average of the 
parental forms. 

Regarding the inheritance of squareheadedness among squarehead x 
vulgare crosses, an idea can be obtained by comparing the Fj-genera- 
tion distributions with the parental distribution (table 5). Special 
attention might be called to the comparatively high degree of square- 
headedness of the Fj generations; in most of the cases the F^ plants are 
almost as squareheaded as the squarehead parents. On a theoretical 
basis the means of the F^ would be expected to coincide with thoie of 
the Fn. The departure here is too wide. This increase in squarehead- 
edness of the F, is attributed both to heterosis and to greater care taken 
in growing and spacing the plants (jf this generatiim. 

The F„-generation distribution, even when the number of individuals 
of which they are composed is considered, shows certain characteristics 
with respect to range of distribution and mean. If the F. distributions 
of squarehead and non-squarehead. crosses are compared with those of 
the crosses in which the parents were either both squareheads or both 
vulgare, it is seen that so far as the mode of inheritance is concerned 
there is no essential difference between them. The means of the F,- 
generation plants shift toward or away from the more squarehead classes, 
but show a constant tendency to regress toward the means of the parental 
forms; and the range of the F2 also spreads or contracts, depending on 
the extent to which the parents vary in degree of squareheadedness. 

Although several of these crosses were carried through the F3 genera- 
tion because of the similarities of the results, only two series are con- 
sidered here, tp illustrate the behavior of the F„ plants in F.^. The 
results of Giant Squarehead -x Fultzo-Mediterranean (series 13140a) 
are shown in table 6, and those of Giant Squarehead x Mealy (series 
13135a) are shown in table 7. 



8i8 



Sarkis Boshnakian 



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Squarehe.-vdedness and Density in Wheat 



819 



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Sarkis Boshnakian 



That a segregation of forms is taking place is (iuite evident. The F3 
distributions shown in table are arranged in the order in which they 
were planted, so that the differences may not be ascribed to environmental 
conditions. Cultures 24-S, 25-3, and 25-4 show notable differences in 
distribution and mean from the cultures growing next tu them. Simi- 
larly, in table 7, where the F, distributions are arranged according to the 
degree of squareheadedness of the F„ plants, the difference in square- 
headedness of cultures 19-17, 19-18. and 19-19, and many others, is to be 
noted. The progeny of plant ig-17, representing a line in which none of 
the plants were squareheads, grew immediately next to a row, 19-18, 
which produced only squareheads, thirty in all. 

In order to show that the variations noted in the F3 are not chance 
variations but are hereditary, the curves shown in figure 78 were plotted, 



l&) 






if 



/^ pro^eoy </ /^ p//fnfs in order tfn/e/t ^liof e^'' ,' . 




Fig. 78. relation of degree of squareheadedness between fs parent hlants 

AND their progeny 



Squareheadedness and Density in Wheat 821 

based on the F3 data of series 13140a (table 6). Two sets of curves 
are shown in this figure. The dotted curve represents the degree of 
squareheadedness of the F._, plants, and the solid curve represents the 
means of the F, in the order of squareheadedness of the F^ plants. 

The inclination of the straight line titted to the curve of the F, prog- 
eny shows that in a general way the degree of squareheadedness of the 
progeny is determined by the degree of squareheadedness of the F^ 
parent plants. A few words of explanation may be given to account 
for the constant rise and fall of this curve. Since the F3 figures repre- 
sent, respectively, the means' of approximately thirty individuals, there 
is no question that they are dependable, and the diii'erences between the 
means of the F3 plants show their comparative genotypic differences. 
Since the mean of the F., in material having a mode of inheritance such 
as this character fluctuates more or less around the degree of square- 
headedness of the F., form planted, it may be assumed that, had the F, 
plants . been grown in the same year as and under conditions similar 
to those under which the F^ were grown, the average degree of square- 
headedness of the developed heads of the F„ planted would have ap- 
proached more nearly the mean of their progeny. Because of the large 
nuniber of plants that had to be measured, it was not found practicable 
to measure several heads from each F^ plant. A developed head was 
taken at random from each of the envelopes containing the heads of 
each plant, and was measured. Since diiferent heads in a single plant 
vary greatly in squareheadedness, the developed head selected at random 
does not necessarily show the true phenotype. Therefore, the zigzag 
nature of the F,. curve should not be ascribed to inconsistent variations, 
but to inability to ascertain the true degree of squareheadedness of the 
Fo by a single measurement, or even more, of the heads of a single plant. 

The difference between the slope of the straight line of the F, curve 
and that of the F, is due to two conditions. In the first place, w^hile 
the Fo curve represents individual plants of a single frequency distri- 
bution, the F.j curve represents the means of such distributions. In the 
second place, as the mean represents the average of all plants exhibiting 
variations, slight or extreme in either direction, the means of the F3 
cannot varv as much as the individuals of the F„ in which the extremes 



822 



Sarkis Boshnakian 



of the frequency distribution are also included. The slope of the fitted 
straight line of the F, means could therefore not be expected to be as 
steep as that of the F„-generation plants. , 

Squareheadedness is not peculiar to the lax form commonly known as 
squarehead. It may be present or absent in other forms also. The 
compactiim forms usually are squareheaded but there are also many 
which are not. In the examples that follow it is shown that square- 
headedness introduced by a club has the same effect on the forms of the 
succeeding generations as does squareheadedness introduced by the or- 
dinary lax squarehead. 

The dense squarehead of the compacto-capitatum form used in this 
study was that known as Dale Gloria (Plate LXVII, upper, 5). This 
form is very dense and has an average internode length varying usually 
from 1.2 to 1.7 millimeters. Its degree of squareheadedness ranges from 
low to high, as shown in table 8. With very dense wheats such as Dale 

TABLE 8. iNHERiT.-kNCE OF Squarehkadedness in a Squarehead x Compactum 

Cross 
(Series 13173a, Dale Gloria x New Soules) 





Degree of squareheadedness 


Mean 


Number 
of 




'0 


§ 


= 




- 


- 





■n 





■A 





10 


° 


iS 


g 


° 


s 


t.- 


^ 







plants 


Dale Gloria 

New Soules 

13173a Fi 


1 


1 


1 


2 


1 




4 


1 




2 




2 
2 
I 
3 


'_1 


'3 
I 
3 


1 

"0 


1 

3 
1 


2 
2 
3 


'2 


'i 
J2 


2 


1.28 
1.71 
1.6.5 
1 46 


17 
15 
4 


13173a F2 








4 




1 


2 


Ji 


_ .■; 


.■i 


4 


41 



Gloria, there is a certain limit beyond which the internodes do not shorten 
further. This is particularly true when the terminal spikelets are fertile, 
for development 'of a spikelet and development of adjacent parts — 
glumes, nodes, internodes — seem to go hand in hand. A slight increase 
in the length of the terminal internodes of heads having an internode 
length in this region as short as 0.8 to 1.2 millimeters, greatly lowers 
the degree of squareheadedness. This accounts for the presence of 
forms of a low degree of squareheadedness among Dale Gloria plants. 

In a cross between Dale Gloria and New Soules ('series 13173a, table 
8), in which both parents were squareheaded, the F„ plants were found 
to be practically all in the squarehead classes. There were a few in the 
non-squarehead classes but these were all dense forms like Dale Gloria. 



SQUAREHEADEDNfiSS AND DENSITY IN" WhEAT 



In a cross such as this, there is also an independent segregation of density 
in the F„ generation. Half of these F„ plants were carried through F3. 
Tiie F, forms were practically all squareheaded. In some cases there 
were a few non-squareheads but these were in a very low proportion and 
probably were genotypically squareheads. As far as squareheadedness 
is concerned, the Dale Gloria x New Soules cross behaved like any 
squarehead x squarehead cross, such as- those shown in table 4 (page 

815). 

When Dale Gloria is crossed with vulgar e forms (table 9), the distri- 

TABLE 9. Inheritance of Squareheadedness in Vulgare x Compactum 

Crosses 

(13214a, Turkey x Dale Gloria; 1337a, Turkish Amber x Dale Gloria; 

13172a, Mealy x Dale Gloria) 









Degree 


of squareheadedness 




Mean 


Kumber 
of 
































in 




m 




10 


r^ 


plants 






00 


35 


OS 

















e^ 




































- 


- 


- 


- 


— 


- 


- 


— 


— 




— 


- 


- 


- 


— 


— 




• 




Parent plants 




























Dale Gloria .... 








1 


1 


1 


■I 


1 




4 


I 




2 




2 








i 






1.28 


17 


Turkey 


2 


3 


2 


2 


1 


3 
































0.92 


13 


Turkish Amber 


1 






3 


li 


10 


ti 


4 


4 


























1.04 


34 


Mealy 








1 


2 


6 


2 


7 


4 


4 


1 


1 




















1.14 


28 


Fi plants 
















































132Ua 


























1 








1 














1337a 
























i 
























13172a 










Not recorded 
































F2 planu 
















































13214a 


1 




5 
2 


4 
1 


11 


10 
6 


•1 

7 


5 


!) 
3 


3 
9 


6 
3 


3 

6 


1 
4 


3 
3 


2 
4 


'2 


2 




"1 




"l 


1.12 
1.2.5 


6.; 


1337a 


64 


13172a 




^ 


2 




2 


6l 31 3 


10 


8 


6 


.=i 


8 


.5 


4 


fi 


4 







2 





1 31 


76 

— . 



butions of both the F^ and F„ generations show a marked resemblance 
to those produced by squarehead x vulgare crosses as shown in table 5 
(page 816). The curves of the F„ in both instances range from the vul- 
gare to the squarehead classes. In this case also Dale Gloria behaved 
as a squarehead; and it is in reality a squarehead, but in addition it hap- 
pens to carry a density factor. 

Two of the crosses in table 9 were carried through F3. The results 
were similar to those already observ*ed in tables 6 and 7 (pages 818 and 
819). Using class i .30 as an arbitrary line dividing non-squareheads from 
squareheads, different F3 progenies produced non-squareheads and 
squareheads in different proportions and degrees. There were progenies 
which consisted of nothing but squareheads, and others which consisted 
only of non-squareheads. 



824 Sarkis Bopiinakian 

The question of the inheritance of squareheadedness, and especially 
that of the relationship of squareheadedness to certain other characters, 
is considered further in the discussion of inheritance of density. The 
general facts observed thus far regarding the inheritance of squarehead- 
edness among forms of the sativum group may be summarized as fol- 
lows: 

Squareheadedness is not a unit character, but is a resultant of a com- 
bination of growth characters which produce shortening of the terminal 
internodes. The F^ and subsequent generations show segregation of 
plants or lines of squareheadedness distinctly varying in degree, but no 
definite ratios are observed among these. The average degree of square- 
headedness of the Fj-generation plants is usually much higher than the 
mean of the F„; in some instances in this study it approached that of the 
squarehead parent. Apparent vigor due to heterosis, and the greater 
care usually given to Fj plants, are considered to account for their varia- 
tion. 

Squareheads crossed among themselves or satk'uius crossed among 
themselves produce, generally speaking, only squareheads or sativmns, as 
the case may be, of ranges and means approaching those of the parental 
forms. The crosses between squareheads and sativmns show a wide 
range of variation, but the range and the mean of the F^ are still deter- 
mined by those of the parental forms. 

Some of the clubs are squareheaded, and these behave as squareheads 
when crossed with other forms. 

RELATION OF THE DEGREE OF SQUAREHEADEDNESS OF THE VUI,GARE 
PARENT IN VUEGARE X SQUAREHEAD CROSSES, TO THE SQUARE- 
HEADEDNESS OF THEIK PROGE-NY 

The question as to the extent to which the parent plants in- 
fluence the squareheadedness of their offspring may be determined by 
examining crosses in which one of the parents is the same in all crosses 
w^hile for the other parent different forms are used. In table 5 (page 816) 
a number of series are shown in which different varieties of vuh/are are 
crossed with Giant Squarehead. The F, and F„ generations of these 
crosses are shown graphically in figure 79, in which the crosses are 
arranged according to the degree of squareheadedness of the vulgare 
parent. 



SquareheadednE-ss and Density in Wheat 



825 



120. 
1.15. 
MO. 
105. 



O/'dat' JfU^re/liiffd ^^aarehe^id fi^rent 




2 0£/y£/?/^r/orf. 



I 
V- 



F 



I 



il 



^ 









I I 



y 



*; 



■^^^9* 



■t:_fK^ 



Wo_ 









/Son-Jauaitihecid parents 






I 

ID 









15 



1^ 






•0 






Series of crosses 



Fig. 79. degree of SQLAREHEADEn.NES.S OF PAKENT.5 AND PROGENY WHEN 
DIFFERENT VULGARE FORMS WERE CROSSED WITH GIANT SQUAREHEAD 



$26 Sarkis Boshnakian 

The curves represeniing the means of both the Fj and F^ generations 
show intermediacy between the parental curves. The F^ curve, as has 
ah'eady been mentioned, sliows, as a rule, a higher degree of square- 
headedness than the Fo. The F„ curve shows a general rise of the 
mean more or less in proportion to that of the vulgare parental curve. 
The Fj curv'e, being based on measurements of very few plants, shows 
great irregularities- although it follows the general lines of the F^ curve. 

The curve to be considered is that formed by the F^ means. Although 
this curve sho.ws a general rise, it cannot be said that the means of the 
F^, increase or decrease directly in proportion with the means of the 
vulgare parents. There are other factors introduced by the vulgare 
parents which, combined with those contributed by the squarehead par- 
ent, tend to neutralize or accelerate the production of squareheadedness. 
For example, Fultzo-Mediterrancan produced an F„ progeny of a very 
high degree of sijuareheadedncss, and the corresponding rise of the. F ^ 
curve shows that this rise is significant. Mealy and Minnesota 169, 
although of a higher degree of squareheadedness, produced individuals 
of lower mean squareheadedness. 

The influence of the vulgare parent on the sijuarcheadedness of vul- 
gare X squarehead-compact crosses is seen in table 9. In the crosses 
in this table the squarehead-compact parent is Dale Gloria. The vul- 
gare parents, Turkey, Turkish Amber, and Mealy, have coefficients of 
0.92, 1.04, and 1. 14. respectively. The ranking of the F, means is in 
the same order, and coincidently the differences between them are in 
proportion with the differences existing between the vulgare parents. 

Because crosses between squareheads produced only squareheads, and 
those between vulgare forms only vulgare forms, it cannot be concluded 
that the degree of squareheadedness of the offspring is entirelv depend- 
ent on that of the parents, for the determining factor is not the degree 
of squareheadedness of the parental forms but the peculiar combination 
of factors introduced by each varietw The mean squareheadedness 
expressed by a yariety is but the resultant of the effects of these factors. 

I'ALSE DnitrNANCE OF SQUAREHEADEDNESS 

Since the F, progen\- of a vulgare x vulgare cross consists only of 
intlgare forms, theoretically one would expect such a cross to produce 



Squareheadedxess and Density in Wheat 827 

onl_y non-squarehcads in Fj. This has not always been the case. In 
table 3 (page 814), giving the results of three Mealy x Jones Longberry 
crosses, the parental means are i . 14 and 1.12, averaging 1.13, and the 
means of the F,-generation plants are i . 12, i . 17, and i . 11, also averag- 
ing 1 . 13. But the Fi-generatio;i plants in all three cases were distinctly 
squareheads, with means of 1.35, 1.50, and 1.42, respectively. In this 
paper the figures for squareheadcdness or for density of F^ plants rep- 
resent the averages of usually from five to ten heads of each plant. If 
the apparent degree of squareheadedness of the Fj plants indicated their 
approximate genotypic make-up, it would be expected that the F„ dis- 
tribution would range somewhat near the mean of the Fj plants. The 
Fj plants in these three cases were all vulgare, showing that the appear- 
ance of Fj plants of a high degree of squareheadedness in these cases 
did not show any type of dominance of squareheadedness. 

These crosses may be contrasted with the Dawson Golden Chaff x 
Pride of Genesee cross (13177a), in which the Fj plants were all xndgare, 
their mean approaching that of the Fj. 

The appearance of squareheads in the Fj generations of series 13158a, 
13178a, and 13179a, and the absence of such forms in 13177a, may be 
accounted for by the supposition that in the first three crosses the com- 
binations of growth factors contributed by the parents were favorable to 
the production of squareheads, while those contributed by the parents in 
series 13177a were not favorable. 

The presence of squareheads in Fj and their total absence in F, in 
series 13158a, 13178a, and 13179a, may be regarded as cases of false 
dominance. 

REL.\TION OF WIDTH OF CULM TO SQUAREHEADEDNESS 

The part of the culm below the base of the spike tends to be wider in 
squareheads than in heads of uniform internode length. The data here 
considered were taken on the progeny of a lax squarehead x vulgare 
cross, which was not as favorable a material for the study of this charac- 
ter as would have been some other crosses in which a more intense 
squarehead was used. The results, however, were satisfactory enough 
to illustrate the degree of correlation between squareheadedness and 
width of culm. 



828 



SaRKIS BOSHNAKIAN • 



In taking measurements for sc|uareheadedness of the F.j generation of 
series 13135a, the width of the culms of some 260 heads was measured 
also. The measurement was taken about 2 centimeters below the basal 
rachis internode. The resulting data are shown in correlation form 
in table 10. The coefficient of correlatiou in this distribution is 0.465 ± 
0.033, which is significant. 

TABLE 10. Correlation between Diameter of Culm and Squareheadedness 
( Series 1313Sa, Giant Squarehead x Mealy ) 
Degree of squareheadedness 
O.S 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.0 1.7 



e 
1«" 



1.4 






1 
















l.t) 






1 
















1.8 


1 


4 


9 


10 


3 


1 




1 






2.0 


1 


11 


25 


28 


12 


8 


1 








2.2 




2 


15 


IS 


8 


5 


4 


4 






2.4 




3 


7 


12 


15 


13 


~^ 


'> 


1 




2.0 






1 


2 





7 


6 


2 




1 


2.8 










3 


1 


2 









ra — ' 



r=0.405±0.033 

The writer considers this correlation as not due to any form of link- 
age but as a direct result of squareheadedness, which is caused in turn by 
the shortening, or rather ham])ering of the development, of the terminal 
part of the spike due to pressure produced b_\' rapid development of the 
culm inlern(j(le immediately at the base of the head, and to the failure of 
the sheath enveloping the spike to grow at a corresponding rate. When 
the longitudinal growth of the culm internode is checked or retarded, 
growth naturally takes place in other directions, often causing a thick- 
ening of the culm wall. A similar thickening of the wall of the culm 
occurs also in non-squarehead dense plants and more pronouncedly in 
squarehead dense plants. In these cases, however, the thickening seems 
to be due to the presence of the density factor, which shortens the culm 
internode length as well as the length of the rachis internode. Due to 
dwarfing, the plant cannot grow in height. The food produced con- 
stantly by the plant is stored partly in the culm, thus increasing the thick- 
ness of its walls. 



Squarehe.\dedness and Density in Wheat 



829 



The club wheat owes its abiUty to stand erect in the presence of strong 
winds to the presence of the density factor, which, as mentioned above, 
produces thickening of the culm and incidentally of other j>arts. This 
factor, which is later considered at length, causes the shortening of the 
culm also, without affecting the number of nodes. The shortening of 
the culm internodes increases the number of nodes to each unit of length, 
thereby giving the culm added strength ; moreover, the shortening of the 
culm lowers the leverage. These three conditions, direct or indirect 
results of the presence of the density factor, are the chief causes of the 
non-lodging quality of dense wheat. 

INHERITANCE OF SQUARE!! EADEHN ESS IN SPELT X SATIVUM CROSSES 

In crosses wherein the spelt character has been introduced, the curve 
of the F„ generation is very distinctly skewed near the extreme of the 
range on the side of the non-squarehead classes (table 11). True spelts 

TABLE 11. Squarehe.\dedness im Spelt x S.\tivum Crosses 























Degree 


of squareheadedness 






















Mean 


Number 





5 


s 



12 

7 




12 
IC 




11 
2 

4 


- 

14 
11 

17 


= 

N 

N 

5 

4 

4 




s 
s 

3 

6 

6 


10 

qua 
qua 

2 

4 

3 


S 

re! 
re! 

I 

2 

2 


lea 
ea 

1 

1 


ds 

is 

7 


3 

1 


5 

2 
2 


-*• 

3 

1 


S 

1 
1 


•0 

m 

1 
2 

2 


2 


in 
to 

1 


2 


1 


00 


^ 


1 


« 


s 

2 


1 



1 


W5 


1 


of 
plants 


13121ja Crimean 
X White Spelt . . 

13260a White 
Spelt X Turkey . 

13216a Giant 
Squarehead x 
White Spelt... 

13255a White 
Spelt X Dale 
Gloria 

3085a Black 
Bearded Spelt 
X Jones Long- 


1 01 

1 10 

1 24 


73 

71 

50 













differ in their ability to carry the factors producing squareheadedness. 
It cannot be determined from the appearance of the spelt plants whether 
or not they carry the squareheading factors, as the spelt character acts 
as an inhibitor for squareheadedness. In fact, the presence of a large 
number of individuals in the non-squarehead classes of spelt x sativum 
crosses is the result of the presence of a large number of spelts, which, 
although carrying the squareheadedness factors, were themselves non- 



830 Sarkis Boshnakian 

squareheads because they carried also the spelt factor, which, as stated 
above, acts as an inhibitor for the squarehead character. 

Five crosses between spelts and sativums are shown in table 11.^ 
Series 13125a and 13260a, which were crosses hetwecnvulgarc and White 
Spelt, produced F, generations composed of non-squareheads only. 
When this same spelt form was crossed with Giant Squarehead (series 
13216a), a number of squareheads were produced in F^. The White 
Spelt X Dale Gloria cross (13255a) also showed a fair number of square- 
heads (Plate LXVII, upper, 6 to 12). 

From these results it is seen that the White Spelt does not carry the 
necessary factors for squareheadedness, since when it was crossed with 
vulgare it produced no squareheads. Squareheads appeared only when a 
squarehead form was used as the sativum parent. 

These four crosses were carried through F.,. The first two crosses 
produced practically no squareheads ; a few were obtained, but they were 
not tested to ascertain their stability. The remaining crosses produced 
F3 progen}- which were composed of forms of various degrees of square- 
headedness. .Since the spelt factor acted as an inhibitor, the spelts of 
the F3 showed no squareheadedness. The non-spelts produced curves 
similar to those shown in tables 6 and 7. 

That there was no so-called repulsion between the spelt and square- 
headedness factors was evident from the reappearance of squareheads 
among the progeny of some F, spelts, and from the absence of square- 
heads among the offspring of other F, spelts. 

Another spelt form, known as Black Bearded Spelt, when crossed with 
a vulgare, Jones Longberry (series 3085a), produced a large number of 
squareheads. These forms were more intensely squareheaded than those 
produced by the White Spelt x Giant Squarehead cross (13216a). 

About ten spelt x vnlgarc crosses, with Black Bearded Spelt as one of 
the parents, were examined by the writer, and in every case there were 
a large number of squareheads in the progeny, most of which were 
semi-dense. 

The progeny of cross 3085a were not carried through F,, but another 



^The F2 segregations. of these crosses were in the proportion of 3 spelts or spelt- 
like forms to 1 sainum. 



Squareheadedness and Density in Wheat 



831 



cross between this same Black Bearded Spelt and a viilgare showed that 
most of the squareheads bred true. 

If it is recalled that some of the F^ spelts of the squarehead x White 
Spelt cross produced squareheads in F3 while others that were phenotyp- 
ically like the former did not, it will not be difficult to understand 
how the Black Bearded Spelt could have produced different results from 
those of the White Spelt. It appears, from these examples, that spelts 
may carry the squareheadedness factors the same as do squarehead 
sativums themselves, but due to the presence of the spelt factor, which 
acts as an inhibitor, such spelts do not appear squareheaded. 

This leads to the consideration of another condition. Since the pres- 
ence of squareheadedness cannot be detected without a genetic analysis, 
one may come across a spelt form which, crossed with vulgarc, may 
sometimes yield squareheads and sometimes not. Either such a spelt 
is heterozygous with respect to squareheadedness, or the variety to which 
it belongs has not been stabilized with respect to this character. As the 
investigator is guided by apparent characters in purifying a line or in 
calling it a pure line, he cannot detect the segregation of non-detectable 
factors which is going on within his selected line. 

EFFECT OF THE SPELT FACTOR ON SQUAKEHEADEDXESS 

In the discussion of the inheritance of squareheadedness in spelt x 
satiznini crosses, it was mentioned that the spelt factor inhibited scjuare- 

TABLE 12. ReL-\TION of SoU.'kREHEADEDXESS TO SpELTIXG 

(Series 13216a, Giant Squarehead x White Spelt) 
Degree of squareheailedness 



00 
o 



a 
o 



o " — 



a 
Q 



1 


.3 


.3 


3 


2 




















1 


*:> 


1 






2 


















1 


1 
2 

1 

1 
2 


1 
3 
2 

1 


1 


2 
1 
3 
2 
1 
2 


2 


1 


1 




1 










1 




1 




1 


1 


2 


1 


1 




1 

2 


2 


1 
2 


1 



83^ 



Sarkis Boshnakian 



a; 

a 



TABLE 13. Relation of Squareheadedness to Spelting 
(Series 1325Sa, White Spelt x Dale Gloria) 
Degree of squareheadedness 

O too »CO >0 lOO »00 OO too lOO »oo»o 
00 00O3 OSO O-^ ^CJ C^CC CC-*** -^O lO^ CJDt^t^ 





o 


o o 


o 


— ' 


'-' 


--1 


—I 


— ' 


— — ( 


rt — 1 


-< 






— ' 


-■ 


rt -H 


1 


3 


3 6 


2 




1 






1 


















?. 


2 


1 3 




2 




2 






















3 




1 1 




3 




2 


1 




1 
















4 








1 


1 


2 






















5 




2 




1 


1 




1 




















6 




















1 














7 








1 






1 




2 
















8 
















. 


















9 
























1 


1 








10 








3 


1 




1 


1 


4 


2 2 


1 




1 


2 


1 


1 



TABLE 14. Relation of Squareheadedness to Spelting 

(Series 308Sa, Black Bearded Spelt x Jones Longberry) 

Degree of squareheadedness 



+ 



o ioo>oo moo 

t^ t^OOQOOS OiOO 





o 


— 


— 


-< 


-' 


•^ 


rt . 


-1 -H _ 


-H -, 


-H — 


-. _ 


-. -. 


-. — - 


H C^ 


04 


1 


2 


5 


1 




1 






















hn2 


1 


2 


2 


2 


1 






















.= 3 




4 




























































- 4 




1 






1 






















a , 
































m h 




y, 




•^ 
























































o H 
































































fi 7 




3 




1 
























S?S 












'} 




















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1 




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1 


2 


2 


1 


1 


1 


3 



headedness. The object here is to show to what extent this inhibition 
takes place. To illustrate this, three types of crosses are used. The 
first is the Giant Squarehead x Wiiite Spelt cross (table 12) ; the second 
is White Spelt x Dale Gloria (table 13) ; and the third is Black Bearded 
Spelt X Jones Longberry (table 14). In the first two crosses, square- 
headedness is introduced by a lax squarehead and a dense squarehead, re- 
spectively, and in the last cross it is introduced by the spelt. 



Squareheadedness and Density jn Wheat 833 

The F2 plants in these tables are classified into ten arbitrary classes 
of spelting. The spelts in such crosses exhibit the spelt character in 
various degrees. Those showing it in an intense form are placed in 
class I ; classes 2, 3, 4, and so on up to 9, show various degrees of dilu- 
tion of the character; the plants in class 10 are all sativum forms, and 
lack the spelt altogether.*^ 

The distribution of the plants with respect to spelting and squarehead- 
edness, as shown in tables 12 to 14, seems to depend to a great extent 
on the types used as parents. Different spelts crossed widi different 
sativums show different modifications. All crosses, however, show the 
following general distribution : Spelts of classes i to 5 inclusive arrange 
themselves more or less within the non-squarehead classes 0.80 to 1.15- 
There is a slight tendency in spelt classes 3 to 5 to move the mean toward 
1.15. As the classes approach the sativum type, the shifting of the 
mean toward the more squareheaded classes is accelerated in geometri- 
cal proportion. 

The spelt factor, then, does not prevent squareheadedness altogether, 
but plants that are heterozygous spelts or those that carry modifiers 
tending to dilute .this spelt character are very much more likely to be 
squareheaded than plants that are intensely spelted. Squareheadedness 
in spelts, however, is always of a low degree. 

INHERITANCE OF SQUAEEHE.\DEDNESS IN SPECIFIC CROSSES 

It has already been shown (page 829) that v.hen Black Bearded Spelt 
is crossed with a sativum of a uniform rachis internode length, an ap- 
preciable number of squareheaded forms appear in the F„. Square- 
heads may be obtained also when a vulgare is crossed with other species. 
In table 15 the progeny of a number of interspecific crosses are classi- 
fied into two groups, the first containing forms resembling the sativum 
type and the second including all the other forms. Their degree of 
squareheadedness is represented in the usual manner. 

In all series a large proportion of the sativum or sativiim-Wkt forms 
were squareheads. The segregates belonging to other species were prac- 
tically all non-squareheads. 



*The genetics of the spelt character with reference to the crosses under consideration 
has been fully discussed in a recent paper (Leighty and Boshnakian, 19:il). 



834 



Sarkis Boshnakian 



TABLE IS. Degree OF Squareheadedness in- Species Crosses. F2 Data 

3032 Salt Lake Club x Kahle (Triiicum durum) 

3034 Gharnovka {T. durum) x Black Bearded Spelt (T. stelta) 

1312a Poole IT. vulgare) x Alaska {T. turgidum) 

1328a Satisfaction (T. vulgare) x Alaska (T. turgidum) 

1360a Jones Paris Prize (.T. vulgare) x Kubanka (T. durum) 



Fa generation 


Degree of squareheadedness 


Mean 


Number 

of 

plants 


results 





» 




» 



d 

4 

3 

7 

2 
8 


S 

'2 

24 

I 
13 


2 

i 
'3 
2 

8 




2 

1 

'4 

1 
1 

1 


'2 

2 

1 

1 
5 


° 

4 

2 

'2 


1 

2 

2 

1 
3 


'2 


6 

i 



5 

2 

1 


1 

2 


2 
1 

i 
1 


2 


I 
1 


!0 

2 

1 

1 

1 
_2 




1 

i 


2 




1 


2 


» 


» 


§ 

2 

2 
1 

4 


3032— 

Sativum and sativum-like 
forms 


1.32 
1.04 

1.81 

99 

1.38 
1,08 

1 69 
1.10 

1.33 
1.5 


35 








1 
'2 


11 


3034— 
5fl(tru»i-like forms * 






5 

36 


1312a— 
Sativum and sa(mm-Iike 






22 






4 


13 


58 


1328a— 
Sativum and sa(iiium-like 




8 


All other forms 


3 


3 


5 


4 


7 


5 

1 
_5 


41 


13ti0a— 
Sativum and sad'vum-like 


9 


All other forms 






_\_ 




_2 


15 



"^Series 3034 did not produce true sativums in tile F2. 
t-.OO or over. 

Squareheadedness is not confined, however, to the sativum form. 
Other species, with the exception of the wild wheat, may show this 
character, particularly the segregates of the durum, the turgidum, and 
the polonicum types and even the diccccum type. But squareheaded- 
ness in these forms is of low degree and is comparatively rare (Plate 
LXVII, lower). 

The analysis of the F, forms in specific crosses presents a difficult 
task because a large number of specific forms appear, of which some 
are developed and others are very mediocre or sterile with different 
tendencies toward squareheadedness. 

SUMMARY 

Squareheadedness, being the result of a combination of growth charac- 
ters, shows a complex mode of inheritance. Simple mendelian segre- 
gations were not obtained in these experiments. 



Squareheadedness and Density in Wheat 835 

In the F3 generation there were obtained plants of different degrees 
of squareheadedness, ranging from forms which were distinctly com- 
pacted at the tip to forms which were denser near the base of the ear. 

As a rule the range of variation in F., depended on the differences be- 
tween the extremes of the parental ranges. The means of the F„ ap- 
proached the parental means. 

The Fj generation usually had a higher coefficient than the parental 
mean. Some Fj progeny of two non-squarehead parems were even dis- 
tinctly squareheads, but in Fj none of these forms were obtained. These 
variations from normal expectations are ascribed to heterosis and to 
greater feeding area. 

A coefficient of correlation of 0.465 ± 0.033 was found between 
width of culms and squareheadedness. 

The purely spelt forms were found not to be affected by the factors 
producing squareheadedness. The more the spelts approached the 
sativum type, the more they were found to be affected. Speltoid forms 
did carry these factors, as is shown by the fact that among their sativum 
progenv a large number of squareheads of varying intensities were 
found. 

Certain spelts when crossed with a vulgare fonn will produce a large 
number of squareheads in F„. Others will produce only non-square- 
headed sativum forms. 

Squarehead forms may be produced by crossing Triticum vulgare with 
other wheat species. 

THE GENETICS OF DENSITY 

The discussion in the following pages deals with the genetics of com- 
pactness of the dense forms of wheat, and especially of Triticum com- 
pactum, the club wheat. The name club zvlieat seems to have been 
originally given to tlie squareheads, but at present it is applied almost 
exclusively to the compactum form. 

The index of compactness used in this paper is the average rachi.s 
internode length. The index is found by dividing the length of the 
rachis in millimeters by the number of rachis internodes. The denser 
or more compact the head, the shorter is the length of the rachis inter- 
node. 



836 



Sarkis Boshnakian 



Although there are numerous grades of compactness, the rachis inter- 
node length of what is usually called a club wheat does not exceed 2.25 
millimeter.-. The mean density of the club used in the studies present- 
ed in this paper was about 1 .4 millimeters. 

INHERITANCE OF DENSITY IN CROSSES BETWEEN TRITICUM COMPACTUM 
AND OTHER FORMS OF THE SATIVUM GROUP 

The studies of density herein discussed were made on crosses be- 
tween Dale Gloria (Plate LXVII, upper, 5) and a number of lax forms 
consisting of both squarehead and vulgare types. The mean density of 
the Dale Gloria parent was i .41 millimeters; the means of the lax parents 
were in the neighborhood of 4.50 millimetA^s. 

The Fj hybrids were all dense, but not quite as dense as Dale Gloria 
(table 16). They varied from 1.80 to 2.40, depending on the cross. 

TABLE 16. Segregation of Density in Crosses between D.^le Gloria (Com- 

paltum) and Lax Forms 
13174a Extra Early Windsor x Dale Gloria 
13173a New Soules x Dale Gloria 
13172a Mealy x Dale Gloria 
13214a Turkey x Dale Gloria 
1321Sa Seneca Chief x Dale Gloria 
1337a Turkish Amber x Dale Gloria 
13213a Red Wave x Dale Gloria 





Degree of squareheadedness 


Mean 


Nusnber 




1.3 


15 


1.7 


1.9 


2.1 


2.3 


2.5 


2.7 


2.9 


3 1 


3.3 


3.5 


3.7 


39 


4 1 


4.3 


4 5 


4 7 


4.9 


5.1 


5.3 


55 


of 
plants 


Parent plants 

Dale Gloria 

Extra Early 
Windsor . . 

New Soules 

Mealy 

Turkey 

Seneca Chief 

Turkish 
Amber ... 

Red Wave. 
Fi plants 

13174a 

13173a 

13172a 

13214a 

13215a 

1337a 


6 


9 

Not 


3 

2 
rec 


2 

4 

jrde 

1 


2 


;; 

I 

I 

5 

'7 
7 
5 

8 
11 


i 
'i 

9 
12 
1 

6 

8 


'3 
6 

1 
2 

4 


i 

4 

'6 
4 


■3 

3 


.. 

1 
1 
2 


'4 
1 

" 
5 
3 
1 

i 


'8 

3 
1 

4 

'5 
1 


3 

5 

2 

2 
2 
4 

■3 


9 

7 

\ 

1 

3 

5 
1 
2 
3 
1 
4 
2 


5 
4 
3 
4 
3 

■ 2 

2 
1 
2 
2 
2 
4 
3 


4 

1 
3 
3 
3 

4 
2 

'2 
4 
2 
5 

2 


3 

'7 
2 
4 

3 
3 

1 

'4 
1 

1 
2 
2 


i 

8 
2 

1 
'2 

'i 
2 


7 
5 

i 
I 


3 

1 

i 


3 

1 

'2 

2 


1 41* 

4 25 

3 89 

4 53 
4 34 
4 48 

4.82 
4 94 

1 80 
1.90 

2.10 
1.90 
2.30 
2.40 

2 59 

2 33 
2.64 
2.74 
2.40 

3 04 
2 87 


18 

24 
30 
14 
15 
11 . 

34 
14 


13213a 

F2 plants 

13174a 

13173a 

13172a 

132Ha .... 
13215a .... 

1337a 

13213a . 


1 
4 

i 


6 
7 
5 
1 
7 
1 
2 


10 
13 
7 
9 
5 
1 
2 


7 
8 
7 
5 
8 
9 
5 


11 
6 
16 

7 

26 

7 

8 


61 
48 
76 
67 
67 
65 



*This figure represents the arithmetical average, not the mean of the frequency distribution. 



Squareheadedness and Density in Wheat 



837 



The density curves of the Fj-generation plants, tniHke those of the 
squarehead x non-squarehead crosses, were all discontinuous, consisting 
of two well-defined curves. In each case the curve of the dense cbsses 
contained about three times as many individuals as that of the lax classes. 
The proportions of these forms are given in table 17. In five cases the 

TABLE 17. Proportioxs of Dense and Lax Segregates of the F-j Gener.\tions 
OF Crosses between Dale Gloria (Comp.a.ctum 1 anp other Lax Forms 





Dense forms 


Lax forms 




























Prob- 


Dev. 


Mean of 


Mean of 


Mean of 


number 
of indi- 
viduals 


Series 










Devia- 


able 




dense 


lax 


all 




Number 


Number 


Number 


Number 


tion 


error 




plants 


plants 


plants 




obtained 


expected 


obtained 


expected 














13n4a 


40 


45,7 


21 


13.2 


--(-5.8 


±2.28 


2.54 


1.88 


3.95 


2 59 


61 


13173a 


39 


36 


9 


12.0 


+-3,0 


±2.02 


1.48 


1.74 


3.74 


2 


33 


48 


13172a 


55 


57,0 


21 


19.0 


—1-2.0 


±2 55 


0.78 


2.11 


4,04 


2 


64 


76 


13214a 


54 


50,2 


13 


16,7 


4—3.7 


±2 39 


1 55 


2.30 


4,51 


2 


74 


67 


13215a 


54 


50,2 


13 


16,7 


+-3.7 


±2.39 


1.55 


1.98 


4,12 





40 


67 


1337a 


43 


48,7 


22 


16,2 


-+5.S 


±2.36 


2.46 


2.34 


4 40 


3 


04 


65 


13213a 


47 


45.7 


14 


15.2 


+-1.2 


±2.28 


53 


2 33 


4 67 


2 


87 


61 


Total 


332 


3.33 7 


113 


111 2 


-+l.f 


±6 16 


29 


2 09 


4 20 


2 66 


445 



deviations from the calculated ratios exceeded somewhat their probable 
errors, and in two cases the deviations were well within the probable 
errors. Summing up the results of these seven crosses, of 445 plants 
obtained in the F, generation ^2i~ were dense and 113 were lax; the 
deviation from the calculated proportions on the 3 :i basis was — -j- 1.8, 
which is about one-third of its probable error. These results show 
that so far as these crosses are concerned the F, plants segregate into 
dense and lax forms in 3:1 ratio, the density being dominant. 

Four of these crosses, of which two were with squareheads and the 
other two with vulgare, were carried through the F3 generation in order 
to test whether the assumption of the presence of one factor was cor- 
rect. The results obtained are condensed and given in table 18. Of 
the 125 F„ plants tested, 30 were homozygous dense, 67 produced both 
dense and lax forms, and 28 were homozygous lax. These figures, com- 
pared with the calculated proportions — 31.2 zt 3.3, 62.5 ± 3.9, and 
31.2 ± 3.3, respectively — show a very close agreement with the 1:2:1 
ratio. The proportion of plants obtained in each cross taken separately 
agrees also with the theoretical expectancy, the largest departure being 
but 25 per cent more than its probable error. 



838 



Sarkis Boshnakian 



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Squareheadedness and Densfty in Wheat 



«39 



The behavior of each individual F. plant of the four crosses under 
consideration is shown respectively m tables 19, 20, 21, and 22. Of the 

TABLE 19. Behavior of F2 Plants in Fs- -Series 13172a, Mealy (Vulgare) x 

D.\LE Gloria 







Mean 


Mean 


Dense plants 


Lax plants 






Prob- n... 




F2 


density 


density 










Total 


Devia- 


able - 


ycv. 


F:; 












pedigree 


density 


of dense 
F3 plants 


of lax 
F3 plants 


Number 
obtained 


Number 
calcu- 
lated 


Number 
obtained 


Numbfer 
calcu- 
lated 


F3 plants 


•tion 


error * 


.E. 


30-n 


1.50 


1.35 




29 








29 








30-21 


1.53 


1,66 




22 








22 


.... 







29-9 


1.57 


1,18 




6 








6 








29-8 


1.65 


1.46 




20 








20 








30-2 


1.71 


1.37 




22 








22 








30-U 


1.73 


1.52 




24 








24 








30-5 


1.76 


1.54 




24 









24 








30-13 


1,81 


1.43 




28 








28 








29-4 


1.89 


1.71 




18 








18 








30-7 


1.84 


1.47 


3.08 


24 


22.5 


6 


7,5 


30 


+ - 15 


±1,63 


) 92 


30-6 


1.85 


1,72 


3 41 


33 


32 2 


10 


10 7 


43 


+ - 0,7 


±1,92 


) 36 


30-9 


1.90 


1 52 


3.01 


34 


33 7 


11 


11 2 


45 


+ - 2 


±1,96 


00 


30-8 


1.95 


1,69 


3.56 


31 


30 7 


10 


10 2 


41 


H — 0,2 


±1 87 


) 11 


29-6 


2.00 


1,44 


3.06 


18 


18.7 


7 


6 2 


25 


— 1- 8 


±1 46 


) .55 


30-19 


2 00 


I 65 


3.00 


23 


21 


5 


7.0 


28 


+ - 2,0 


±1.55 


29 


29-10 


2.06 


1 80 


3 70 


25 


24.7 


8 


8,2 


33 


-1— 0.2 


±1 68 


) 12 


30-3 


2.10 


1,67 


3.53 


28 


27,0 


8 


9.0 


36 


+- 1,0 


±1,78 


) 56 


29-3 


2.11 


2 08 


3 30 


19 


15 7 


2 


5,2 


• 21 


-1 — 3 2 


±1 34 


; 39 


30-13 


2.14 


1 70 


3 33 


34 


36,0 


14 


12 


48 


—1-2 


±2 02 


) 99 


29-12 


2,19 


2.04 


4.03 


92 


18 7 


3 


6 2 


25 


H — 3 2 


±1.46 


M9 


30-20 


2,25 


1 83 


3.64 


22 


24 7 


11 


8 2 


33 


-+ 2,8 


±1.68 


1 67 


29-1 


2 39 


1 90 


3.15 


18 


16,5 


4 


5 5 


22 


+- 15 


±1 37 


1 09 


29-11 


2 42 


1.72 


3,69 


30 


29,2 


9 


9 7 


39 


+ - 0,7 


±1.82 


3 38 


30-10 


2.43 


1 93 


3 52 


32 


27,7 


5 


9 2 


37 


4— 4,2 


±1.78 


2 36 


30-1 


2.50 


2.22 


4 23 


37 


35.2 


10 


11,7 


47 


+ - 17 


±2 00 


3 85 


30-15 


2.52 


1.85 


3 47 


28 


25 5 


6 


8,5 


34 


-t— 2,5 


±1 70 


1,47 


29-2 


2 53 


2.00 


3 64 


19 


19 5 


7 


6 5 


26 


— h 0,5 


±1.49 


3 33 


30-4 


2 58 


1 81 


3,56 


27 


23 5 


11 


9 5 


38 


-+ 1,5 


±1 80 


3 83 


29-14 


2 84 


1.78 


4 26 


13 


13 5 


5 


4 5 


18 


— 1- 0,5 


±1 24 


3 40 


Total hete 


rozygoua pii 


ints .... 




517 


501 7 


1.52 


167 2 


669 


-1—15 2 


±7 55 1 


2 01 


30-16 


3.28 




3.39 






16 




16 










30-12 


3.55 






3 36 






23 




23 












30-22 


3 75 






3.12 






20 




20 












30-17 


3.84 






3,43 






17 




17 












29-13 


4,16 






3,88 






20 




20 












29-5 


4.27 






.8.65 






17 




17 












29-7 


4 44 






4 08 






5 




5 












Total F3 


plants , . , , 










1 


1 


1 980 




1 1 


^=^1= 



669 heterozygous plants obtained in series 13172a (table 19), 517 were 
dense and 152 were lax, the deviation from the calculated ratio being 
about twice its probable error. In series 13173a (table 20), the ratio 
between the probable error and the deviation from expectation is i : 5 . 22, 
which is rather high. In series 13174a (table 21) this ratio is 1:5.62, 
and in series 13214a (table 22) it is only i :o.46. All these results, in 
spite of the differences between observed and calculated ratios which 



840 



Sarkis Boshnakian 



TABLE 20. Behavior of Fo Plants in F3. Series lol74a, New Soules 
(Capitatum) X Dale Gloria 







Dense plants 


Lax plants 










Fa 


F2 










Total 
F3 plants 


Deviation 


Probable Dev. 


pedigree 


density 










error p_ jj_ 






Number 


Number 


Number 


Number 














obtained 


calculated 


obtained 


calculated 










32-7 


1 31 


37 








37 








31-11 


1.52 


23 










23 










32-6 


1,52 


• 60 


.'. . . 








60 










31-3 


1 55 


40 










40 










31-9 


1 55 


35 










35 










32-8 


1 62 


41 










41 










31-8 


I 64 


24 


27 8 


13 


9 2 


37 


—1- 3.8 


±1.78 2 


13 


32-13 


I 65 


52 


58 5 


26 


19 5 


78 


— f 6.5 


±2.58 2 52 


32-14 


1 68 


51 


54.0 


21 


18 


72 


— h 3.0 


±2 48 1 


21 


31-7 


1 71 


29 


31 5 


13 


10 5 


42 


-+2.5 


±1 89 1 


32 


32-15 


1.71 


93 


99 8 


40 


33 2 


133 


— f 6 8 


±3 37 2 


02 


32-9 


1.78 


67 


67 5 


23 


22 5 


90- 


-+ 5 


±2 77 18 


32-16 


1.81 


59 


63 


25 


21 


84 


—1-4 


±2 68 1 


49 


31-12 


1.88 


35 


32 3 


8 


10 7 


43 


+- 2 7 


±1 92 1 


41 


32-5 


1 91 


46 


46 5 


16 


15 5 


62 


— t- 0.5 


±2 30 22 


32-10 


1 95 


62 


63 


22 


21 


84 


-+ 10 


±2 68 37 


31-1 


1 95 


30 


43 5 


28 


14 5 


58 


-+13. 5 


±2 22 6 08 


32-2 


2.00 


42 


39.0 


10 


13 


52 


+-3 


±2 11 1 


42 


31-2 


2.06 


40 


39 8 


13 


13 2 


53 


H — 0.2 


±2 13 09 


31-4 


2 09 


30 


33.0 


14 


11 


44 


-+ 3 


±1 94 1 


55 


32-12 


2.15 


83 


87.8 


34 


29 2 


117 


-+ 4 8 


±3 16 1 


52 


32-17 




62 


69 8 


31 


23 2 


93 


-+ 7 8 


±2 82 2 


76 


Total heterc 


zygous plan 


ts 805 


. 856 5 


337 


286 5 


1.142 


-+5 


5 


±9 87 1 5 


22 


31-10 


3 40 






37 




37 






.... 1 




31-6 


3 43 






21 






21 












32-4 


3 45 






56 






56 












32-3 


3.80 






69 






69 












32-1 


3 87 






31 






31 












31-5 


3.95 






33 






33 












31-13 


4 19 






24 






24 












32-11 


4 28 






71 






71 













Total F3 plants 



they exhibit occa.sionally, show, that so far as these crosses are concerned 
only one factor is involved in the production of density. 

Referring to tables 19, 20, 21, and 22, it will be noticed that while in 
series 13172a and 13214a the proportion of dense and lax forms agreed 
rather closely, in series 13173a and 13174a an excess of lax forms was 
recorded in practically every case. In series 13173a, out of 16 heter- 
ozygous plants tested all but three yielded an excess of lax forms, while 
in series 13174a all but one plant yielded an excess of lax forms. 

When wheat plants are grown closely together, the roots occasionally 
tend to intertwine, and unless the heads show variations of segregating 
gross characters it is not usually possible to determine whether there are 
two plants or only one. In crosses between dense and lax plants, in 
which the segregation is 3:1, out of 16 possibilities there are 9 chances 



Squareheadedness and Density in Wheat 



841 



TABLE 21. Behavior of Fo Plants in Fa. Series 13174a 
Extra Early Windsor CCapitatum) x Dale Gloria 











Dense plants 


Lax plants 














Mean 


Mean 














Prob- 


Dev. 


F2 




density 


density 












Devia- 




P.E. 


pedigree 


density 


of dense 


of lax 




Number 


Number 


Number 


F3 plants 


tion 


error 






F3 plants 


F3 plants 


obtained 


calcu- 
lated 


obtained 


calcu- 
lated 










3t-3 


1 31 


1,29 




29 








29 








34-8 


1 40 


1.28 




25 








25 








34-11 


1 55 


1 36 




22 








22 








33-5 


1 55 


1.28 




46 








46 








33-1.5 


1,85 


1.30 




46 








46 








33-9 


2 00 


1 28 
1,37 




39 








39 








33-4 


1,70 


3,09 


59 


64 5 


27 


21 5 


86 


-+ 5,5 


±2 70 


2 04 


33-2 


1 74 


1,57 


3.77 


56 


63 7 


29 


21.2 


85 


-+ 7 8 


±2 69 


2 90 


34-4 


1 86 


1,57 


3 69 


31 


32,2 


12 


10.7 


43 


-+ 13 


±1 92 


68 


34-6 


1 95 


1,54 


3 31 


23 


24,0 


9 


8.0 


32 


-+ 1,0 


±1,65 


61 


Itf 


1 95 


1,69 


3 33 


23 


24 


9 


8 


32 


— 1- 10 


±1 65 


61 


2 00 


1,39 


3 32 


18 


17 2 


5 


5.7 


23 


+ - 7 


±1.40 


50 


33-6 


2 00 


1 54 


3 59 


49 


51 7 


20 


17 2 


69 


— t- 2,8 


±2 43 


1 15 


33-7 


2 00 


1 60 


3 34 


45 


48 


19 


16.0 


64 


-+ 3 


±2.32 


1 29 


33-3 


2 00 


1 60 


3 42 


45 


50.2 


22 


16 7 


67 


— f 5 3 


±2 39 


2 22 


33-13 


2 05 


1 60 


3 80 


47 


48,7 


18 


16 2 


65 


-+ 1,8 


±2 36 


76 


34-10 


2,11 


1.69 


3.48 


23 


24 


9 


8,0 


32 


— f 10 


±1 65 


61 


33-17 


2 20 


1,57 


3 53 


48 


52 5 


22 


17,5 


70 


-+ 4,5 


±2 44 


1 84 


33-11 


2 21 


1 65 


3.50 


51 . 


57 


25 


19,0 


76 


-4-6 


±2 55 


2 35 



Total heterozygous plants . 



I 518 I 5.58 I 226 I 186.0 



1 — H40 01 ±7 ' 



33-10 

34-1 

33-1 

34-9 

34-7 

33-16 

33-12 



3 30 




3 20 








22 




22 








3 50 




3 35 








34 




34 








3.71 




3 35 








35 




35 








3 95 




3 36 








18 




18 








3 96 


.... 


3,62 








24 




24 








4 05 




3 33 


.. 






42 




42 








4 42 




3.77 








51 




51 


•■ ■ 







Total F3 plants 



1.177 I 



that a dense plant will grow next to a dense plant, 6 chances that it 
will grow ne.xt to a lax plant (or that a lax plant will grow next to a 
dense plant), and i chance that a lax plant will grow next to a lax plant. 
In other words, where entangling exists due to close planting, there will 
be six cases in which this condition will be detected and lax and dense 
plants separated, and nine cases in which it will be overlooked because 
the heads will all be dense and will show no visible difference. If this 
factor of entanglement is present whereby some dense plants are over- 
looked, theoretically there will be fewer dense plants than are expected. 
If the degree of experimental error introduced by this factor is cal- 
culated, it will be found that if, among 50 plants forming a segregating 
population, there are two or three cases in which a dense plant has been 
interlaced with its neighbor and is not separated, the differences between 
recorded and theoretical ratios will be about as great as those shown in 
tables 20 and 21. 



84:; 



Sarkis Boshnakian 



TABLE 21. Behavior of F2 Plants in Fs. Series 13214a, Turkey (Vulgase) 

X Dale Gloria 











Dense plants | 


Lax plants 














Mean \ 


lean 












Prob- 


Dev. 


F2 


F- 


density df 


nsitv 








— Total 


Devia- 


able 


P.E. 


pedigree 


density 


of dense o 


flax" 


Number 


Number ^^ 


[,ljjr Number F3 plants 


tion 


error 






Fs plants F3 


plants 


obtained 


c"'™- obtJ 
lated 


ined ra'™- 
lated 








38-8 


1.72 


1.46 




68 






68 


.... 






39-9 


1.91 


1,76 




45 






45 










38-12 


1.95 


1 41 




97 






97 










38-14 


1.95 


1 49 




85 






83 










39-4 


2.06 


I 66 




33 






33 










38-11 


2 16 


1.51 




59 






59 










38-9 


2 33 


1 61 




83 






83 










38-13 


2.39 


I 58 




57 






57 










38-4 


2 75 


1 49 




44 






44 










40-3 


1.57 


1.37 


IS 


73 


57 8 


4 19 


77 


H — 15.2 


±2,56 


5 94 


40-6 


2 11 


1 65 


(23 


47 


41 3 


8 13, 


55 


-H- 5.7 


±2 17 


2 63 


38-15 


2. II 


1.58 


i 20 


35 


40 5 


9 13 


> 54 


— i- 5.5 


±2,15 


2,56 


40-1 


2.28 


1.64 


i.l5 


42 


48 


!2 16 ( 


) 64 


— V 6,0 


±2.34 


2,56 


39-3 


2.35 


1.67 


! 28 


29 


31,5 


3 10 . 


> 42 


— f 2.5 


±1.89 


1 32 


40-2 


2,35 


1,91 


!.51 


53 


54 8 


!0 18 


> 73 


-- 1- 1.8 


±2 50 


0,72 


39-2 


2.53 


I "6 


) 44 


52 


51 7 


7 17. 


> 69 


— 1- 0,2 


±2.39 


08 


38-2 


2.53 


2,08 


1 30 


10 


12 8 


7 4 


17 


— 1- 2.8 


±1 20 


2 33 


40-7 


2 57 


1,92 


i.77 


46 


42 


14 


) 56 


-1— 4.0 


±2.19 


1.83 


38-10 


2.61 


1 96 


! 51 


30 


30 


10 ( 


) 40 


0.0 


±1,85 




39-5 


2.75 


1.87 


).32 


24 


23 3 


7 7 


1 31 


-h- 0.7 


±1 63 


043 


40-8 


2.79 


2.13 


!.78 


48 


58 5 


iO 19 


) 78 


--H0.5 


±2 58 


4 07 


38-5 


2.89 


2.16 


1.09 


23 


24 


9 8 ( 


) 32 


— H 1.0 


±1 65 


61 


38-7 


2,90 


2.23 


i.72 


47 


45 


3 15 ( 


) 60 


H — 2.0 


±2 26 


0.88 


40-4 


2 94 


2.18 


i.59 


48 


45 8 


3 15 


! 61 


-f- 2.2 


±2 28 


96 


40-10 


3.00 


2 20 


i.83 


51 


48,8 


4 16 


! 65 


-1 — 2.2 


±2 36 


93 


39-6 


3 06 


2.28 


i,89 


73 


71 3 


!2 23 


1 95 


+ - 1.7 


±2 85 


60 



Total heterozygous plants 



I 731 I 726 7 I 238 1 242 2 I 960 |-h- 4 21 ±9 09 I 



38-3 

38-1 

38-6 

39-1 

38-16 

40-5 



4.06 




3,94 






37 




37 






4.11 




4 57 






12 




12 






4.14 




3 75 






41 


• • . . 


41 






4.21 




3 41 






32 




32 






4,59 




3,78 






58 




58 


1 


5 29 




3 64 






91 




91 


. , , , , , , , 1 



Total F3 plants 



In crosses 13173a and 13174a, density was the only visible dift'eren- 
tiating character; hence the separation of the entangling plants depended 
merely on that character. In series 13172a and 13214a, in which the 
experimental errors were practically as much on one side as on the other, 
the error due to entangling was reduced, respectively, bv the introduction 
of the pubescent glume character through the Alealy jiarent, and by the 
color of chaff and the beardedness introduced by the Turkey parent. 
The introduction and consequent segregation of these characters enabled 
the author to detect the presence of more than one plant, and through 
their separation the degree of experimental error in these two sets of 
crosses was greatly lowered. 



Squaeeheadedness and Density in Wheat 



843 



INFLUENCE OF THE DENSITY OF THE LAX PARENT IN A LAX X COMPACTUM 
CROSS OX THE DENSITY OF SUCCEEDING GENERATIONS 

In connection with table 16 (page 836) the reader perhaps noticed that 
there was a tendency- on the part of some Fj and Fg generation fre- 
quencies to be shifted somewhat toward the laxer classes while others 
tended to shift toward the denser classes. Since the dense parent (Dale 
Gloria) was the same in all seven cases, these variations, if hereditary 
to any extent, should be ascribed to the influence of lax parents which 
represent the variable factors. 

The mean densities of parent and offspring are represented graphically 
in figure 80. The curves are arranged in the ascending order of the 




/^eeJn densiTy of 
- lax p>i^rents 

"1 /V(?^/3 dens'iTy of 



^■J7i-'^°\./^e?j/2 c/easify of 

, /Ve^/2 dens/fy of 
V - ' --L-^^^ ^e^fa densJ/y of 



Fig. 80. influence of density of lax parent on density of fi- and fs- 
gexeration plants 



844 Sarkis Boshnakian 

densities of the lax parents. The straight Hnes fitted to the curves show 
a general rise; that is, with the increase of the average internode length 
of the lax parent, the averat^e internode length of the Fj and the Fj 
increase more or less in the same proportion. 

The slopes of the fitted lines for the F,, the total Fj, and the dense Fj 
segregate, are practically the same, being 0.089, 0.086, and 0.090, re- 
spectively. Those for the lax parents and the lax F, segregates show- 
also a general rise but of a higher degree. It should be borne in mind 
that the higher the class values, the greater is the tendency of the curve 
toward a higher inclination. 

The curves representing the densities of the Fj and the dense F, 
segregates follow each other very closely. The other curves also follow 
the same general course. Evidently the material representing the cross 
with Mealy was somewhat denser, because both the Fj and the F^. curve 
show a similar rise at that point. The rise of the Mealy parent is not 
in the same proportion. 

Aside from these differences, it should be noted that the values of Pi 
and Fj are higher because they represent crops grown in different years 
and also because they were spaced more widely than the F„ plants. Be- 
sides, the Fi perhaps shows vigor due to heterozygosis, which, together 
with increased food supply due to the wide distances between plants, 
tends to increase the size of the spike without increasing the number of 
spikelets, which in turn tends to increase the average internode length. 

RELATION OF DENSITY OF F, PLANTS TO THAT OF THEIR PROGENY 

The comparison of the density of F, and of F., plants leads to the 
decision as to whether the variations in density, especially of the F^ 
heterozygous plants, are hereditary or represent mere fluctuations due 
to external conditions. To be sure, environmental conditions, as is 
pointed out in the first part of this paper, have a great mfluence on the 
degree of density. The plants used in this experiment were grown on a 
small area, and consequently the environmental factors had practically 
as much opportunity to affect the density of one plant as that of another. 

In comparing the density of the F, plants with that of their progeny, 
series 13214a may be taken as an example. Deductions based on this 
cross will apply as well as for the other crosses. The mean densities of 



Squareheadedness and Density in Wheat 



«45 



the F; parent and the offspring, as shown in table 22, are represented 
graphically in figure 81. Comparison of the density curves of the F, 
plants with the mean density curves of their progeny shows that, espe- 
cially in the case of the heterozygous F„ plants, there is a correlation 
between the density of the F, and that of their F3 segregates. Since there 
is such a correlation between F. and F., ihese apparent fluctuations are 



s.z 

50 
















■ 


















1 

1 
































1 \ 


i -> 


1 
1 

1 


















\, 












/ 
/ 




















1 ' 




/ 


\ 






\ 






^ -7.6 














/-- 


1 


\ 


1 


N 


' 




lnjf 


k / 

5> 


■09 


532 












^ "'1 


A 


'lux 


/^ />roye 


V 
















, 






H^r^r, 


izy^u 


us ^ ,- 'deasi 


1 — •• 












ftomoi 
































-' 


L--- 






/"" 




/\ 


A 


— -^ 


r 














7.^ 


/^ 


y 




■/ens 


t 


r 




fomo - and /ieti!ro7j/(jou5 K dense broken 

1 1 1 1 ■ 1 ' , ■ 


y 











»0 ^ ^ ^ vfi l^ 

i <a ta & oa A 
■o ■O n "^ '^ ^ 



Fig. 81. comp.\risox of density of fj with that of dense (homozygous 
or homozygous and heterozygous) and la.x progeny 

liereditary variations. It goes without saying, then, that these F. heter- 
ozygous plants are not genotypically identical with respect to compact- 
ness, and that, although all the F„ heterozygous plants have the general 
formula Cc, they carry besides this factor a group of other factors which 
tend to increase or decrease compactness. 

relation of density of dense and lax segregates of heterozygous 

F^, plants 

The presence of factors modifying the degree of density may be fur- 
ther demonstrated by a comparison of the curves of the dense segregates 



846 Sarkis Boshnakian 

with those of the lax segregates. This test is made on the assumption 
that if a group of modifiers is introduced there will be as much chance 
for these to be transmitted to the dense segregates as for them to be 
transmitted to the lax forms of the progeny of heterozygous dense F, 
plants ; in other words, both dense and lax forms will receive the same 
dose of modifiers. Accordingly, if a set of modifiers shifts the mean of 
the dense segregates, say about five classes, toward a plus or a minus 
direction, the mean of the lax segregates should be shifted likewise, to 
the extent of as many classes at least, and very likely more, toward the 
same direction. 

On examining the density frecjuencies shown in tables 23, 24, and 25, 
it will be noted that whenever the dense segregates of F^ heterozygous 
plants are grouped toward the laxer classes the curve of the lax segre- 
gates corresponding to them tends also to arrange itself in that direction, 
and vice versa. For example, in table 23 (series 13214a), of the progeny 
of 40-3 the dense forms are very dense, with a mean density (table 22) 
of 1.37. The density of the lax form is 3.18. Comparing this with 
the progeny of 38-2, the mean of whose dense segregates is 2.08 and of 
the lax 4.30, it may be seen that whatever interfered with the compact- 
ness of the dense plants of 38-2 afifected also the density of the lax forms. 
Throughout tables 23, 24, and 25, in which the details of the frecjuency 
distributions are given, the same phenomenon may be observed. The re- 
lation between the mean density of the dense segregates and that of the 
corresponding lax segregates of the F^ progeny of each heterozygous 
F„ plant of series 13214a (table 22) is shown graphically in figure S2. It 
is seen in these graphs that with the increase or decrease in the density 
of the dense plants, the density of the lax forms varies in the same direc- 
tion. This is a direct evidence that besides the density factor there are 
also modifiers affecting the degree of density within the dense and the 
lax classes. 

GENERAI, COXSIDKRATION ON THE FREQl'ENCY PrSTRIBUTIONS OF COMPACT 

X LAX CROSSES 

Each dense x lax cross has its own peculiar type of fretjuency distri- 
bution, either in the first or in later generations. The type of distribu- 
tion seems to depend on the density of the parents concerned and on the 



Squareheadedness and Density in Wheat 



847 



^22 

ho 

^/8 



/-/omo7.y(^ous /sx seg/'^Q3Tes 




FlC. 82. RELATION OF PENSITY OF DENSE AND LAX SEGREGATES OF 
HETEROZYGOUS F2 PLANTS 



848 Sarkfs Boshnakian 

set of modifying factors introduced by them. In the discussion of table 
16 (page 836) it was brought out that lax plants differ from one another 
in degree of density, and that the density of their progeny varies accord- 
ing to the density of the lax parent, the dense parent being the same. As 
to the question of modifiers, the frequency-distribution tables 23, 24, and 
25 show the characteristics of the curves of each cross. 

In series 13214a (table 23), although there is a gap between the dense 
and lax curves, in a number of cases this gap is not so evident. In figur- 
ing out the ratios the determination of the possible line of separation was 
a matter of judgment in some cases. Series 13172a (table 25) shows 
a wider gap. To a very small degree the fewness of the plants may 
account for it. The plants of series 13174a (table 24) show a much 
wider gap and the presence of two definite curves is at once seen. In 
crosses between dense and lax forms, all gradations between a distribu- 
tion such as is shown in series 13174a, and a continuous skew curve, may 
be obtained. 

Crosses made between semi-dense squareheads (often classified as 
clubs) and lax forms produce an uninterrupted curve which makes it 
practically impossible to separate them into dense and semi-dense, and 
lax genetic, classes. 

Regarding the mendelian classifications of segregating lines such as 
those produced by the heterozygous F„ plants of series 13214a, it will 
not be out of place to make a few remarks. Some workers on this sub- 
ject have taken a certain class of density as a dividing line between dense 
and lax forms, presumabl}- based on the classes of least frequency of the 
F^ curve. While such a method may be more or less satisfactory in a 
cross similar to series 13174a (table 24), it is absolutely unjustifiable in 
genetic studies and unsuitable for the great majority of crosses in which 
dense or lax forms appear. In the first place, since F^ and F, plants are 
grown in different years they do not necessarily show the same degree 
of density. This is shown in table 23. There is practically no heter- 
ozygous plant of the F3 generation which produced a curve similar to 
that of the F„. Theoretically about half of the F,, curves should have 
approached the F„ curve. The "reason for this failure lies in the fact 
that the F, plants were grown under more favorable environmental con- 



Squareheadedness and Density in Wheat 



849 



1 

'b 

a 
IS 

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ii 



Squareheadedness and Density in Wheat 



851 



Average internode length (in millimeters) 


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852 Sarkis Boshnakian 

ditions than were the F3. Now if, for example, density class 3.2 based 
on the Fj curve (table 23) is taken as the dividing line and is used for 
separating the dense and lax forms of the F3, it will be noticed that a 
large number of lax forms of the F3 will be included in the dense class. 

It has been mentioned that each F^ curve has its peculiar mode of dis- 
tribution- In tables 23 and 25 it is shown that the frequencies of some 
dense curves extend beyond the classes where the curves of some lax 
forms have begun. The peculiarity of each curve necessitates the tak- 
ing of each curve and the separation of the dense from the lax forms 
at the class or the probable class of least frequency. If the density 
curves of segregating forms are not prepared, more trustworthy results 
can be obtained by classifying the forms by eye than by taking an arbi- 
trary dividing line. This latter method can be used in cases in which the 
variations are discontinuous. 

In specices crosses, discontinuous curves are the exception rather than 
the rule, and separation of dense and lax forms into two genetic classes 
by an arbitrary dividing line has no meaning because such a separation 
cannot be made even by the e.Kamination of the curves, even disregarding 
the fact that some specific forms which carry the density factor may 
be laxer than most of the vulgare forms. 

That density is a dominant character and is inherited in the 3:1 ratio 
has been shown by Spillman (1902), Strampelli (1907), Wilson (1907), 
Von Tchermak (1910), Nilsson-Ehle (1911), Mall (1912), Parker 
(1914), and others. The three last-named have called attention to the 
fact that forms laxer and denser than the parental types are obtained 
also in compactum x zndgare crosses. 

The use of the word squarehead for semi-dense forms by some au- 
thors accounts for the disagreement of their results. Von Riimker 
(1909) obtained from compact x non-compact crosses, compact, square- 
head, and vulgare forms in approximately the ratio 1:2: i. No doubt 
the "squareheads," which proved to be heterozygous, were heterozygous 
club forms. Von Ritmker cites another case in which the F^, segregated 
into dense and lax forms approximating 3:1, there being no squarehead 
forms. The heterozygous forms in this cross could not be distinguished 
from dense forms. 



Squarehe;.\dedne:ss and Density in Wheat 853 

Biffen's (1905) results, which are often cited as contrary to those ob- 
tained by others, seem rather to agree with Von Riimker's. Such differ- 
ences as exist are due to methods and nomenclature. Biffen crossed 
Squarehead's Master with Red King, the average internode lengths being, 
respectively, 3.2 and 4.6 millimeters. The Fj hybrid ears averaged 4.8 
millimeters in internode length, and the F._, ranged from 3.2 to 5 milli- 
meters. In this early work the frequencies are not given, but it appears 
that the distribution was of the normal, or skew, type. Using 4.6 (the 
mean of Red King, or the internode length of this lax parent) as the 
dividing line, Biffen found that 78 plants were laxer than the lax parent 
and 22 were intermediate between the dense and the lax parent, while 
there was no form denser than Squarehead's Master. From this result 
Biffen concluded that in this case laxness was dominant. In the first 
place. Squarehead's Master, with an internode length of 3.2, does not 
fall in the compactum class and the cross should not be included in that 
category. In the second place, the use of the density of the lax parent 
as the dividing line seems to be too arbitrary and unjustifiable from a 
genetic standp)oint. 

Neither does Biffen's Rivet x Polish cross fall in this category, since 
it does not belong to the sativum group. In crosses of this type specific 
segregations occur which greatly complicate ratios. His Devon x Hedge- 
hog cross is of the semi-dense coinpactum x lax type. The photographs 
shown in the article cited, and also bv Bateson (1909:23), show that 
the Fj is intermediate dense and the F^ evidently approximates the 3 : i 
ratio, the heterozygous forms being slightly laxer than the dense parent. 

Biffen's results, then, so far as the compactum x lax cross is con- 
cerned, may be regarded as being in accord with similar work done by 
others. 

Since dift'erent types of dense and lax forms have been used Iw various 
investigators, their results with respect to degree of density have been 
different. Segregation into two distinct curves is obtained as the degree 
of density of the parents approaches the extremes of the dense and lax 
classes. As a rule, the closer the parents approach in degree of density, 
the more continuous the curves will be. This statement applies for 
crosses made within the sativum group. The existence of several factors 
producing varying degrees of density is evident. 



854 



Sarkis Boshnakian 



THE NATURE OF DENSITY FACTORS 

Three questions of special interest arise, regarding the nature of the 
density factors producing varying degrees of density in so-called pure 
lines. They are: (i) Is the density of the coinpactmn type caused 
by but one factor pair, and are the degrees of density produced by the 
presence of modifiers? (2) Do the forms varying in degree of density 
carry different density factors allelomorphic to one another, or (3) Are 
they caused by multiple factors ? 

A considerable amount of work has yet to be done to answer these 
questions definitely, as numerous genetic analyses are necessary. A few 
suggestions based on experiimental results can be made, however, regard- 
ing the probable nature of these density factors. 

The results of all the compacium x lax crosses reported thus far show 
the presence of but one density factor; a 15:1 ratio has not yet been 
obtained. But in crossing a compactum with a somewhat dense vulgare, 
not infrequently forms are obtained which are laxer than the vulgare 
and denser than the compactum parent. For the sake of simplicity in pre- 
vious discussions, this occurrence was ascribed to the presence of modi- 
fiers. The writer believes that these modifiers are secondary factors 
representing varying degrees of density. The factorial combinations 
according to this hypothesis, and their corresponding phenotypes, may be 
illustrated in the following manner : 



Pi 



CC dd X cc DD 

compactum slightly dense vulgare 







CcDd 










compactu 


m slightly 








1 


axer than i 


Icnse parent 






1 CCDD 


1 CCdd 


2 Ccdd 


1 ccDD 


2 ccDd 


1 ccdd 


2 CCDd 


2 CcUD 

12 compactum 


4 CcDd 




4 vulgare 




3 denser 


2 approxi- 


6 laxer 


1 same as 


2 slightly 


^ 

1 much 


than 


mately of 


than 


vulgare 


laxer 


laxer 


dense 


same den- 


dense 


parent 


than 


than 


parent 


sity as 


parent 




vulgare 


vulgare 




dense 






parent 


parent 




parent 











Squareheadedness and Density in Wheat 855 

In the preceding outline, C stands for the high degree of compactness 
introduced by the coinpactnin parent, and D for the shght degree of 
compactness exhibited by the vulgare parent. This hypothesis accounts 
for the production of stable forms CCDD denser than the com pactum 
parent and ccdd laxer than the vulgare parent. 

In instances in which lax stable forms somewhat denser than the lax 
parent appear, the phenomenon may be explained according to the same 
hypothesis. If the above extreme dense CCDD and lax ccdd forms taken 
as parents are crossed, stable forms denser than (•<•</(/ will lie obtained 
according to the factorial combinations. 

If there are different factors of density producing the coinpactum 
type, certain crosses between two compactuni forms should give i in 
16 or I in 64 lax forms. Let it be supposed that the compactuni parents 
have the genotypic forms CiCjCoC^, and c-^c-^C^C, where there are two 
different C factors. With two factor differences, one plant out of six- 
teen in the F„ should have the c^c-^c^c^ constitution, therefore being very 
lax. The writer knows of but one cross between two club forms, and 
from that cross, among 130 F, plants no lax forms were observed, al- 
though considerable variations were found within ,the dense classes. 
In this case both parents seemed to be homozygous for the same C factor ; 
and the C factors contributed by both parents either were identical or 
belonged to the same allelomorphic series. 

The author has evidence that the density factor of the coinpactitm 
type may belong to a multiple series. The Black Bearded Spelt carries a 
density factor which may be isolated by crossing it with a lax vulgare 
form. About three-fourths to one-half of the F„ vulgare forms are 
dense and semi-dense. In five such crosses the results have been simi- 
lar. This shows that a C factor is carried by this particular spelt. If 
this factor is identical or forms an allelomorphic series with another C 
factor, the F, satizntnis segregating in a cross between this spelt and a 
club should be all dense. The fact that in such a cross lax sativum 
forms also are occasionally obtained, shows that in this case there were 
two distinct C factors involved. 

Another C factor is carried by the dicoccuiii form known as Black 
Winter Emmer. When this form is crossed with a vulgare it throws 



S56 Sarkis Eoshnaktan 

a certain proportion of distinctly dense sativum individuals. The F^ 
plants from eight such crosses were examined and compact forms were 
recorded in every case. As in the preceding instance, in tlie F„ derived 
from two Black Winter Emmer x club crosses, consisting of 
about 150 Fj individuals, soft lax vulgare types could be counted, al- 
though most of the sativum types were dense. Here again it appears 
that, as in the preceding cross, two different non-allelomorphic multiple 
C factors were introduced. 

Summarizing the foregoing discussion, it is apparent that: 

1. There are density factors each producing shortening of the rachis 
internode in different degrees. These max be present in addition to 
the compactum factor. 

2. There is as yet no sufficient evidence tliat some compactum factors 
may form an allelomorphic series. Neither is there any evidence that 
such series may not exist. 

3. There exists in wheat more than one density factor belonging to 
multiple series. If such multiple density factors are present, eventually 
15: I, 63: I, and other ratios will be obtained from compactum x vulgare 
crosses. 

FACTORS PRODUCING SQUAREHEADEDXESS AS COMPRISING ONE OF THE 
GROUP OF FACTORS MODIFYING DEGREE OF DENSITY 

A modifier, as generally held, may be a factor affecting a particular 
character quantitatively, the presence of which is detected from the 
degree of modification of the character which it modifies. In a broad 
sense, however, any factor or character whose presence affects or even 
inhibits more or less the expression of another character should be re- 
garded as a modifier. 

The irregularities among the F,. density curves of dense x lax 
crosses shown in this study were ascribed to the presence of modifiers, 
as the genetic analyses applied to the crosses showed conclusively the 
presence of but one density factor. Proofs that these variations were 
hereditary, and not caused by environmental conditions, were also given. 

The nature of one of these modifiers, the character for squareheaded- 
ness, may here be considered. In crosses in which a non-squarehead was 
involved, it was noticed that there was an independent segregation of 



Squareheadedness and Density in Wheat 



857 



density and squareheadedness, and that whenever the latter character was 
present, whether the plant was dense or lax, there was, as a rule, a 
reduction of the average internode length. 

Density notes derived from series 13172a are summarized in table 26. 
This cross, it will be recalled, is between Mealy, a lax non-squarehead, 

TABLE 26. Mean Density of F3 Lax Plants Classified According to 
Proportion of Squareheads and Vulgare Forms. Series I3I7-<1 



AU squareheads 


More squareheads 
than vulgare 


Squareheads = vulgoTe 


More tnlgnrf 
than squareheads 


.\U vdgare 


Pedigree Density 


Pedigree 


Density 


Pedigree 


Density 


Pedigree 


Density 


Pedigree 


Density 


30-19 


3 00 


29-1 


3 15 


29-3 


3.30 


29-5 


3 65 


29-2 


3 64 


30-22 


3.12 


29-6 


3 06 








29-14 


4 26 


29-7 


4.08 






29-13 


3,88 








30-1 


4 23 


29-10 


3.70 








30-6 


3 41 








30-8 


3.56 


29-11 


3 69 








30-7 


3 08 








30-10 


3 52 


29-12 


4.03 








30-9 


3 01 








30-16 


3 39 


30-3 


3 53 








30-12 


3.36 








30-17 


3.43 


30-4 


3. 56 








30-13 


3.33 












30-15 


3 47 






















30-20 


3 64 


Mean and i 


















3vera2eerror|3.06±0 04 




3,28±0.07 




3 30 




3.72±0 11 




3 71 ±0 05 



and Dale Gloria, a dense squarehead. In this cross both density and 
squareheadedness segregated independently. The table shows the density 
of the lax forms of the Fj-generation lines arranged in five classes, 
according to the observed proportions of squareheads to non-squareheads. 
In the first class are included the F3 plants which consisted of square- 
heads only ; the second class includes the pedigrees that produced more 
squareheads than vulgare forms; the other three classes represent 
progenies consisting of an equal number of these two forms, of an excess 
of vulgare, and of only vulgare, respectively. 

By averaging the degree of density of each group it is found that 
the average internode length increases inversely with the proportion of 
squareheads. The average internode length of the squareheads was 
3.06 ± 0.04, while that of the plants producing an excess of squareheads 
was 3.28 ± 0.07. The densities of the class yielding more vulgare than 
squareheads and that producing only vulgare were 3.72 ± o.ii and 
3.71 it 0.05. respectively. The dift'erence in the av'erage internode 
length of the extreme classes was 0.65 ± 0.06. Comparison in terms of 
the average of the means of these two classes, shows this difference be- 



S58 Sarkis Bosh nak IAN 

tween the density of pure .squareheads and that of pure vulgarc to be 
equal to about 20 per cent of their means, which is rather remarkable. 

Were tlie lax plants of the F,, generation all or practically all square- 
heads, one would expect the elimmation of variations as great as those 
found in the crosses between inihiarc and dense scjuareheads. Series 
13174a (table 24, page 850), which represents a cross between a square- 
head and a dense squarehead, shows the absence of shifting of the curves 
back and forth, so evident in tables 23 and 25, which represent dense 
squarehead x vulgarc crosses. , 

Vlthough the variations introduced by the presence of both vulgare 
and squarehead forms is eliminated in cross 13174a (table 24), other 
modifiers must be present because the curves still show inheritable varia- 
tions. The nature of these remaining modifiers is not as yet known. 

It is not difficult to explain how squareheadedness increases density. 
Pliysiological studies show that squareheadedness, which is brought about 
by the shortening of the terminal internodes, is due to contact and pres- 
sure caused l)y the differential rate of growth of parts of the plant 
surrounding the spike during its earlier periods of growth. If, during 
the process, the terminal internodes fail to attain their normal size, that 
part of the head will be denser than it would have been if the plants 
were allowed to grow normally. This .-hortening of internodes of the 
terminal part of the head is the direct cause of the decrease of the 
average internode length of the entire head. 

RELATION OI-' SQUAREIJEADEUXESS TO DENSITY IN Fo-GENERATION PLANTS 

The modes of inheritance of squareheadedness and of density have 
been discussed separate!}' herein. It is necessary now to illustrate the 
relation between these two characters m crosses in which both of these 
characters have been introduced. Series 13172a, 13214a. 1337a, and 
13173a (tables 27, 28, 29, and 30, respectively), which have already 
been considered, will be used again as examples, because each illustrates 
a different mode of inheritance. 

Before examining the behavior of the F^ plants, the distribution of the 
parent plants with respect to density and squareheadedness may be 
reconsidered. This distribution, although based on few numbers, is shown 
graphically in figure 83. The plants recorded do not represent samples of 



Squareheadedness and Density in Wheat 



859 



■Sau^re/i endedn ess 

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X 


X 




















































































Fig. 83. distribution of parental plants with respect to 
density and squareheadedness 



the varieties used in making the crosses'; they are the progeny of each of 
the plants used as parents. 

Dale Gloria, it is seen, is distributed within a very narrow range with 
respect to density, but within a wide range with respect to squareheaded- 
ness. This latter range does not represent the genotypic range of the 
variety, if one may be allowed to use that expression. The length of the 
rachi^ itself is about 2 to 3 centimeters. If the terminal spikelets are ster- 



86o 



Sarkis Boshnakian 



lie, as often happens in dense clubs and less frequently in lax forms, this 
sterility and rudimentary condition will keep the terminal rachis inter- 
nodes from developing furtiier while the other internodes continue their 
growth. A head of this type will have a high coefficient of square- 
headedness. If, on the contrary, the terminal florets develop vigorously, 
the increase in the size of the grain will tend to stretch the internodes 
somewhat. With a vigorous growth of the grain is associated a relative 
growth of the adjacent internodes, and with as short a head as that of 
the club in question it does not take much increase in internode length 
to lower the squareheadedness of some individuals down to classes 
i.oo to 1 .25. 

The distribution of New Soules is entirely different from those of 
the other lax plants used in the crosses. It is somewhat more toward 
the denser classes and falls distinctly within the squarehead classes. 

Turkish Amber is a vulgare, but its average internode length is great- 
er than that of any other of the forms represented. 

TABLE 27. Rel.\tion of Squareheadedness to Density' in Fa Segregates. 
Series 13172a, Mealy x Dale Gloria 
(Mean dense plants, D=2 01, Sq.=1.34; mean lax plants, D=3.95, Sq.=1.23) 

Squareheadedness 





c 








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Squareheadedness and Density in Wheat 86i 

Mealy has practically the same distrihution as Turkish Amber but i» 
somewhat less lax. • 

Turkey is the least lax in the vulgare group and is located \erv much 
toward the non-squarehead classes. 

The mode of inheritance which might generally be expected in com' 
pactum X vulgare crosses is that of the Mealy x Dale Gloria series 
(table 27), which shows a wide range of distribution with respect to 
squareheadedness. Theoretically, since Dale Gloria carries the factors re- 
sponsible for squareheadedness and Mealy does not, both density and 
squareheadedness would be expected to segregate independently, which 
happens in this case. Using, for practical purposes, class 1.30 or 1-35 
as a dividing line, it is seen that there are about as many individuals on 
the side of squareheadedness as on the side of non-squareheads. By 
using as a guide the distribution of the Mealy parent shown in figure 83, it 
becomes very evident that in this cross the character of squareheaded- 
ness has been introduced among the non-squareheads. The mean value 
of squareheadedness of the lax parent is 1.14 and that of the lax plants 
of the cross is 1.23, showing an increase of 0.09. While out of 15 
Mealy parental plants (figure 83) there was but one individual in the 
squarehead classes in the F„ generation, out of a total of 20 plants there 
were about four or five times more individuals in these classes. In 
table 26, which represents the same cross, it has been shown that some 
of these lax squareheads remained stable. 

The distribution when Turkey was the lax parent (table 28) was 
strikingly dififerent from that in the case of Mealy. In the Turkey x 
Dale Gloria cross, no lax squareheads appeared. 

On comparing the dense classes of tables 27 and 28 with respect to 
their squareheadedness distribution, it is seen that the entire distribution 
has been shifted to the left in the latter table. The mean squarehead- 
edness of Dale Gloria is 1.28; that of the dense plants of the cross is 
1. 17, showing a shifting of o.ii toward the non-squarehead classes. 
While the squareheadedness of the dense form is afifected by that of the 
lax forms, the diiTerence in the coel?icients of the lax parent and the 
lax segregates, these being 0.92 and i.oo, shows that the lax segregates 
are in turn influenced to some extent by the squareheadedness of the 
dense parent. 



S62 



Sarkis Boshnakian 



TABLE 28. Relation of Squareheadedness to Density in F2 Segregates. 

Series 13214a, Turkey x Dale Gloria 

* 

(Mean dense plants, D=2.18. Sq.=1.17; mean lax plants, D=^.23, Sq.=1.00) 

Squareheadedness 






•n 





IQ 





lO 





iO 





»0 





oe 


CO 


as 


03 












(N 


M 


n 





000 





-H 


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—1 


— 


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-^ 


-^ 


T-l ,-H 


•-1 


1.5 






















1 


1.7 




1 


1 


1 




2 






1 


1 




1.9 




1 








1 




1 


2 






2.1 










1 


1 


2 


2 




1 




2 3 








1 




1 


1 


2 






1 


2.5 






4 


1 


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3 








1 




2 7 


2 


1 


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1 






1 




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2.9 


1 






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2 
















3.3 
























3 5 
























3.7 
























3.9 
























4,1 


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1 




1 












4.3 


1 




1 


















4.5 






2 


2 
















4 7 




1 




















4 9 


1 




1 


















5.1 
























5.2 






1 



















In the cross in which Turkish Amber was used (table 29), the square- 
headedness of the lax segregates occupies practically the same position 
as that of the lax parent itself, the values of squareheadedness of the lax 
parent and the lax segregates 'being 1.04 and 1.07, respectively. This 
slight shifting toward the non-squarehead classes may well be disregard- 
ed. Unlike the condition in the preceding cases, the dense forms showed 
no visible effect of the lax parent. The mean squareheadedness of the 
dense segregates, instead of being less, was slightly greater than that 
of the dense parent and practically the same as in series 13172a. 

In the fourth cross (table 30) the lax parent was New Soules, a dis- 
tinct squarehead. The lax segregates of this cross were all squareheads, 
and with regard to density they occupied the same position as the lax 
squarehead parent (figure 83). 

Incidentally it should be noted from this table that, while the range 



Squareheadbdness and Density in Wheat 



863 



TABLE 29. Relation of Squareheadedness to Density in F2 Segregates. 

Series 1337a, Turkish Amber x Dale Gusria 

(Mean dense plants, D=2.23, Sq.=1.35; mean lax plants. D=4.30, Sq.=107) 

Squareheadedness 

o looioo »oo ioo»oo 00 100 00 »oc 

Oi OSOO^H ^HC^ CICCCCI* -t^O OCO ot^ t^oo 





c 





— 


— 


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1.5 












1 


















1.7 
















1 














1.9 












1 


1 


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1 1 






1 


2.1 










1 


1 


1 


1 


1 




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1 


1 






1 




2.7 


















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2.9 










1 


1 


1 




1 


1 










3.1 






















1 


1 1 






3.3 






























3.5 






























3.7 










1 




















3.9 






1 




1 










1 










4.1 


1 






1 


1 






1 














4.3 




1 




1 


1 


1 


















4.5 


1 




1 


2 








1 














4.7 








2 






















4.9 






1 
























5.1 






























5.3 






























5.5 






2 

























of density of the dense segregates of other crosses extends as far down 
as class 3.1, that of this cross (table 30) is confined within classes 1.3 
to 2. 1 with but one individual in class 2.5. This difference is accounted 
for by the higher degree of density of New Soules (figure 83) as com- 
pared with those of the other lax forms. 

Recapitulating the points of interest brought out in the discussion of 
these four tables, the following general deductions can be made : 

1. The factors of density and those of squareheadedness are totally 
independent of each other. They segregate and reconibine independ- 
ently. 

2. The wheat varieties of the satwum group have different degrees of 
density and of squareheadedness. Even among the vulgare plants this 
latter form of compactness, as measured by its coefficient, varies. In 



864 



Sarkes Boshnakian 



TABLE 30. Relation of Squareheadedness to Density in F2 Segregates. 

Series 13173a, New Soules x Dale Gloria 

(Mean dense plants, D=1.64, Sq.=1.43; mean lax plants, D:=3.64, Sq.=1.59) 

Squareheadedness 



1.3 


1 




1 




















1.5 


1 






2 




1 


1 








1 


1 


1.7 


2 


1 


1 


1 


1 




1 




1 


1 


1 




1.9 




1 1 


1 




'> 


I 














2.1 








1 


1 




1 




1 


2 






2.3 


























2.5 








1 


















2.7 


























2.9 
















1 










3.1 


























3.3 


















1 1 








3.5 


















1 


1 
















1 
















b.7 
























3.9 












1 














4.1 












1 














4.3 
























1 



crosses in which one parent is the same, not all vulgare nor all square- 
heads nor all dense forms produce a frequency distribution of square- 
headedness or of density of the same type and within the same range. 
Whether the range will remain approximately in the same location, or 
will shift one way or the other, is determined to a great extent by the 
degree of squareheadedness or of density of the different forms of 
vulgare or squareheads, as the case may be, which are involved in the 
cross. 

3. There are exceptions to the general rule stated above. In series 
1337a there was a visible segregation of density but not of squarehead- 
edness. In this case there was evidently interference by another factor. 

Nilsson-Ehle (1911) considers the inheritance of squareheadedness 
and gives a factorial explanation to account for the apparent proportion 
in which it appeared in some of his crosses. But, while Nilsson-Ehle 
used the term squar*ehead for la.x forms — which have a comparatively 
shorter average internode length than the vulgare forms — that term is 
applied in the present paper to forms showing a relative density of the 



Squarehe.'Ujedkess and Density in Wheat 865 

middle and the upper third of the spike of about 1.33 or over, irrespec- 
tive of the average inteniode length. It is not possible to compare Xils- 
son-Ehle's results and hypothesis with those from this study. 

RELATION OF LENGTH OF RACHIS TO DENSITY IN HY'BRID PLANTS 

Lengtli of rachis is dependent on two factors, namely, the number ot 
internodes and their length. If the number of internodes in a popula- 
tion is more or less constant, as has been the case in all the crosses be- 
tween Dale Gloria and other forms considered herein, the length of the 
rachis is directly proportional to the average internode length. This 
is so obvious that it needs no illustration. 

If both factors are made variable by the selection of parents which 
var}' both in number and in length of internodes, then there is no cor- 
relation between length and density. As an illustration a cross may be 
cited which was made by the writer for this purpose. This cross was 
Silver Club x Aegilnps ovata. Silver Club (Plate LXVII, upper, 3) is a 
club wheat from four to five centimeters long, with about seventeen to 
twenty internodes. The Aegilops (Plate LXVII, upper, i) also was 
short, like the cliib wheat, but had only six internodes of an average 
length of about six to seven millimeters. The basal internodes were the 
shorter, their spikelets being rudimentary. ' 

Unlike the parents, the Fj plants all had long heads, resembling the 
spelt wheat. Three plants obtained in the F, also were lax. The point 
of interest in this cross was that the F, and F„ plants did not inherit 
length of rachis from their parents, but number and length of internodes. 
The Fj heads usually had from twelve to fourteen internodes from six- 
to seven millimeters in length. The three F. plants showed some varia- 
tion in length. In the Fj 'plants, both characters being intermediate, the 
heads were necessarily much longer than in either parent. It would be 
expected, if sufficient Fj plants were obtainable, that the plants would 
segregate with respect to both characters into short heads dense and lax, 
that is, with many and with few internodes, and also comparatively long 
heads dense and lax, with possible intermediate forms. 

In this connection it may be pointed out that what has been called 
vigor due to heterosis in wheat is. often the appearance of unusually 
long heads in Fj or later generations in crosses with certain emmers. 



866 Sarkis Bosiinakian 

These are, as a rule, somewhat dense and bear some thirty internodes to 
the spike. Hence the question is rather one of number of internodes 
and internode length. The plants that combine the internode length of 
the vulgare parent with the number of internodes of the emmer must 
necessarily be unusually long. 

In actual practice, in a cross such as the above a considerable number 
of synthetic spelts appear. These spelts have the peculiarity, as is shown 
later, of producing internodes longer than those of the lax parent. The 
appearance of this new type helps to increase the proportion of un- 
usually long heads. 

RELATION OF LE-NGTH OF CUI.M TO EACH IS LENGTH AND DENSITY 

In a pure line of wheat there is practically no correlation between 
culm length and density, but there is a correlatioii between culm length 
and length of rachis. The plant that prodvices a short culm due to un- 
favorable environmental conditions naturally produces a small head ; 
but such a head as a rule has fewer rachis internodes than the mean of 
the line, and therefore, although the undeveloped head is short, its 
density has not been affected to any extent because the number of rachis 
internodes has decreased more or less proportionately. 

The writer's studies of the relation of culm length to density were 
made on series 13214a, because this line produced practically no square- 
heads. Squareheading, it has been shown, unless it is due to favorable 
growth conditions, has a tendency to shorten the average rachis internode 
length. There being no squareheads in the material used, that factor 
was eliminated. 

The question of the relation of culm length to other characters of the 
head is of interest from both the economic and the genetic viewpoint. 
Because of the many phases to which this problem of density has led, 
it was not possible in this investigation to study the relation of culm 
characters as intensively and extensively as the subject deserves. Suffi- 
cient data have been obtained, however, to give an idea of the general 
liehavior of this character. 

Due to the great variability of culm length, the preliminary studies 
were made with a number of progenies of F„ plants each of which had 
yielded on an average about 60 individuals. The frequencies of the 



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868 



SaRKIS BtiSHNAKIAN 



tliree characters, culm length, rachis length, and rachis internode length, 
are shown in table 31, together with then- means. The F3 lines included 
m this table are arranged according to the order in which they were 
planted— 38-3, 38-4, 38-5, and so on, representing successive rows of 
plantings. An inspection of the table shows that these three characters 
— length of culm, length of rachis, and average internode length--are 
more or less closely correlated. As a rule the lines with long culms pro- 
duced lax plants and those with short culms yielded dense plants. It is 
seen from the curves in figure 84, prepared from the data in table 31, that 




Culm 
Rifchls 



Pcdiqree 






ryfi^ 
























Fig. 84. average culm, rachis, and internode length of some F3 

FAMILIES OF SERIES 13214a 

'^''^ nrlilf„f,1''' i'^^.V^'a'ion of culm length to rachis and u.ternode length, 
order of the families corresponds to the order in which they were planted 



The 



Squareheadedness and Density in Wheat 869 

when the mean of one of the characters decreases or increases, the 
others vary as a rule in the same direction. 

There being no inherited variation in number of internodes (which 
averages about 20 to the spike) in the F3 hnes, the curves of rachis length 
and average internode length follow each other very closely. The 
curve of the culm length, although in a general way varying with density, 
shows certain irregularities, especially in the case of lines 38-6 and 
40-4. The former is a homozygous lax type and the latter is heterozy- 
gous; yet the mean culm length of the former is considerably less than 
that of the latter, although theoretically it should have been greater. 
The possibility of the effect of environmental conditions being out of 
the question, it appears that there is a segregation of culm length inde- 
pendent of the dwarfing caused by the presence of the C factor. This 
statement is made as a suggestion only, since at the present time no def- 
inite explanation can be given. 

A fact which seems rather interesting is that the C factor does not 
shorten the culm length in the same proportion as it shortens the rachis 
length. The averages of the rachis and culm lengths of the homozygous 
lax (cc) plants were about 7.7 centimeters and 89 centimeters, respec- 
tively. The presence of the double dose of the C factor (in 38-4, 38-8, 
and 38-9) shortened the rachis length to an average of 3.2 centimeters 
and the culm length to about 74 centimeters, a shortening of 58 and 17 
per cent, respectively, from the general average. In other words, while 
the rachis length was shortened by the C factor by more than one-half, 
the culm length was shortened but one-sixth. 

Studies of the characters of dense and lax segregates ha\^ led the 
author to believe that the C factor is a dwarfing factor, shortening, be- 
sides the culm length, the rachis length, and the rachis internode length, 
a number of other characters such as length of gkimes, length of kernels, 
length of awns, and length of culm internodes. These two last-named 
characters have not been studied carefulh- by the author. Sapehin 
(1916) and his collaborators, who studied the correlation between density 
and culm internode length, claim that there is a significant positive cor- 
relation between these two characters. From the present studies it 
seems apparent that the shortening of the culm as a result of the pres- 



8/0 Sarkis Boshnakian 

ence of the factor for density, is due not to the reduction in number of 
culm internodes, but to the reduction in length of the cuhii internodes, the 
number of these , internodes remaining more or less constant. In 
this respect the phenomenon of the shortening of the culm is similar to 
that of the shortening of the rachis. It has been demonstrated by vari- 
ous workers that in maize also dwarfing causes the shortening of the 
internodes of the stalk without necessarily affecting their number. 

In a general statement such as is made here regarding the presence 
of a correlation between density of the head and shortness of the culm, 
it is not intended to convey the idea that dense plants or varieties are 
all to be short, and lax plants tall. The cardinal points brought out are 
(i) that when the factor of density or its absence has been introduced 
in a progeny through hybridization, provided there are no interfering 
factors, the dense plants will be more likely to have short culms than 
the laxer plants; and (2) that this shortening of the plant is caused, not 
by the reduction in number of culm internodes, but by the reduction 
in their length. It should be borne in mind, however, that these charac- 
ters are affected by environment. From a genetic viewpoint the exhi- 
bition of a quantitative character in an individual plant is of little value 
especially if this is affected by environment. The comparative height 
of a plant is determined by the behavior of its progeny. 

CORRELATION BETWEEN AVER.\GE INTERNODE LENGTH AND LENGTH OF 

STERU.E GLL'MES 

One of the proofs that the density factor is a dwarfing factor is found 
in the high degree of correlation existing between the average internode 
length and the length of the sterile glumes. The material for the study 
of this correlation consisted of the spelt plants of series 132553-15, rep- 
resenting a cross between Dale Gloria and White Spelt. This F, line seg- 
regated into dense and lax sdfk'uiiis and spelts. In the data here only 
the spelts are represented. The spelts were selected primarily because 
the glumes could be readily removed from the spikelets, as they break 
off uniformly at the base of the glume at a definite region just below the 
heel. With vuU/are forms the taking of measurements is somewhat 
more laborious. The measurements of the glumes recorded here rep- 



Squareheadedness and Density in Wheat 



871 



resent the average of the length of opposing sterile glumes on the same 
spikelet at a distance from the base of the spike of about one-third the 
length of the rachis. This precaution was taken because the glumes 
shorten as they approach the distal or the basal part of the head. 

The correlation between average internode length and glimie length is 
represented in table 32. The correlation coefficient here is 0.838 ± 

TABLE 32. Correlation between Density and Length of Sterile Glumes 
(Series 13255a-15, Dale Gloria x White Spelt; only the spelts measured) 

Length of glumes (in millimeters) 
6.5 7.0 7.5 8.0 8.5 9 9 5 10.0 10 5 



a_ 

0} CD 

a a 



> 
< 



1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 
5.0 
5.5 
6.0 



1 


1 

3 
3 
1 


1 

6 

1 


3 


2 
1 
2 












• 




1 


2 

1 


1 
1 

1 


1 
1 


2 

1 
1 


1 
1 



r = 0.83S±0.039 



0.039, which shows significantly that in this particular cross the factor 
decreasing rachis internode length is the one causing the shortening of 
glumes. The relation of density to glume length may be readily seen on 
heads 6, ~, and 8 in Plate LXV'II (upper), which show the grades of 
density and consequently of glume length. 

CORRELATION BETWEEN AVERAGE INTERNODE LENGTH AND LENGTH OK 

KERNELS 

The same degree of correlation exists between density and length of 
kernels as between density and glume length. The measurements of 
the length of the kernel as here recorded represent the average length of 
the first and second kernels developed on the basal florets. Of these two 
kernels the first was very often longer than the second. In cases in which 
either the first or the second basal floret had not produced seed, the third 
seed was not measured in its stead because the third seed is always likely 



872 



Sarkis Bosiinakian 



to be smaller. In such cases a different spikelet was chosen, the samples 
being taken always at a distance from the base of the head of about 
one-third the length of the rachis. 

Correlating these two characters as shown in table 33, a correlation 

TABLE 33. Correlation between Density and Length of Kernels 
(Series 1325Sa-15, Dale Gloria x White Spelt; only the spelts measured) 

Length of kernels (in milHrneters) 





5.6 


5.8 


6.0 


6.2 


6.4 


6.6 


6.8 


7.0 


7.2 


7.4 


7.6 7.8 


:g 1-5 
^ 2.0 


1 


1 




1 


1 

1 




1 










-?2.5 

■il 3.0 
E e 3.5 


1 






2 
3 


5 
1 


1 
1 

1 


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5 




2 




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1 


1 




1 







coefficient of 0.747 it 0.024 \- 



r = 0.747±0.024 

obtained. Compared in terms of the 
respective probable errors, this is as high as or slightly higher than the 
correlation between density and glume length. 

The width of the kernels was not atfected by the length of the kernels 
or by density. This density factor does not seem to produce diminu- 
tiveness but to shorten along one axis only. The width of the kernels, 
whether taken laterally or dorsi-ventrally, remaining practically the same, 
the shape of the kernels assumes a spheroid form among the dense seg- 
regates and a long spindle form among the lax plants. 

Since density is correlated with length of glume and length of kernel, 
it is obvious that in this material there is also a direct correlation between 
length of glume and length of kernel. 

KELATION OF DENSITY OF RACHIS TO DENSITY OF RACHILLA 

A rachilla is the rachis of a spikelet, and branches out from the main 
rachis. A spikelet may have three or more rachilla internodes ; the 
basal one is very short, but toward the terminal part of the spikelet the 
internodes elongate and then shorten again. 



Squarehe.\dedi\ess and Density in Wheat 



873 



It is practically impossible to measure the average rachilla internode 
length. For comparative purposes, however, the relation of density to 
average rachilla internode length can be determined indirectly by noting 
the extent of the protrusion of the fertile glumes of the florets. The 
relative distance between the fertile glumes of the first and the third 
floret on different wheat heads indicates their relative rachilla inter- 
node length, as is illustrated in figure 85. 






Fig. 85. spikelets of spelts of v.^rying degrees of density, showing relation of 

INTERNODE LENGTH (.X, -X'. AND x") TO LENGTH OF STERILE GLUMES ( Y, y', AND y" ) 
AND REL.\TIVE R.\CHILLA INTERNODE LENGTH AS DETERMINED BY DISTANCE BETWEEN 
THE TIPS OF THE FERTILE GLUMES OF THE FIRST ."iND THIRD FLORETS (z, z', .^ND z") 



To l:>ring out the correlation between rachis and rachilla internode 
length it is necessary to find a population comprising wheat plants of 
the same species which are segregating into dense and lax forms. 

Dense and lax spelt plants of series 132553-15 are reprersented, respec- 
tively, in A and B of figure 85. The illustration shows that the laxer was 
the form, the more did the florets protrude above the two sterile glumes. 
In figure 85, C, is represented the appearance of a synthetic spelt of un- 



8/4 Sarkis Boshnaktan 

usual length derived from a durum x lulgare cross. It shows a further 
increase in rachis internode length, together with a relative increase in 
glume length. 

These observations, which unfortunately cannot be presented in the 
usual form of a correlation table, indicate that C, the factor for com- 
pactness, shortens also the length of the rachillae or that of their inter- 
nodes. 

THE FACTOR FOR SPELTIXG ACTING AS A MODIFJER FOR THE DENSITY 

FACTOR 

Density, like squareheadedness, is affected to a large extent by the 
presence of the spelt factor. In series 13255a, which represents a cross 
between White Spelt and Dale Gloria ( I'late LXVII, upper, 4 to 12), there 
is but one spelt factor. Spelts and sativums segregate in this cross in the 
simple monohybrid ratio of 3 spelts of all grades (heads 6, 7, and 
8) to I sativum (which includes compactum [heads 9 and lol, square- 
heads [head 11], and rulgarc [head 12]). In a cross in which 
one of the parents is a spelt, the inheritance of density cannot be studied 
if all the plants are classified according to density alone, for, as will be 
seen, in the presence of the factor for spelting the factor for density 
does not produce compactness in the same degree as it does in the ab- 
sence of the spelt factor. Therefore, in determining the mode of in- 
heritance in such cases, it is necessary to take into consideration both 
the degree of spelting and the density, and in interpreting the data the 
density curves of the spelt and those of the sativums should be examined 
separately. 

The difference in density of the spelt and the Sativum form may be 
best illustrated by the density curves of the progeny of the two F^ plants, 
one of which was homozygous dense and the other was homozygous 
lax, but both of which segregated into spelts and sativums. The relatiVe 
density of spelts and satimwis is shown in table 34. The plants of 
132553-26 are segregates from the Dale Gloria x White Spelt cross. 
They are all homozygous dense, but are derived from F„ plants heter- 
ozygous for the spelting character. If S stands for the spelting factor 
and C for compactness, the F, progeny of line 132553-28 consists of 
SScc, Sscc, and sscc individuals, while 132553-26 consists of SSCC, 



Squareheadedness and Density in Wheat 



875 






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8/6 SaRKIS BoSHNAKrAN 

SsCC, and ssCC plants. The mean internode length of the lax spelts, 
as shown in table 34, was 4.22 millimeters; that of the sativunis was 
2.76 millimeters, showing a difference of 1.46. Of the plants homio- 
zygous for the density factor, the dense spelts had a mean internode 
length of 2.00 millimeters and the dense safh'iiins one of 1.57, showing 
a difference of 0.43 millimeter. 

From these results it is seen that, although the internode length of the 
spelts can be shortened by the introduction of the C factor, the presence 
of the ,S" factor tends to interfere with the effect which a known C fac- 
tor would otherwise produce. 

The relation of the 5 factor to density is the same as the relation of 
this same factor to squareheadedness. It has already been shown that 
the presence of factors for squareheading have a very slight effect on 
the heads that carry the factor for spelting. 

THE SYNTHETrC PRODUCTION OF TRITICUM COilPACTUM 

Triticiim compactum, as has already been shown, is but a fonn of 
Tr. sativnin, which carries an additional factor or factors for compact- 
ness. The results of crosses between different species show that this 
same factor can be carried as well by any of the other species of 
Triticum. In fact, there will be found in commercial strains species 
that carry density factors, though not necessarily the same factor. Many 
forms of durum, and especially of dicoccum, carry a density factor. 
When these are crossed with a lax I'ulgare form, compact forms invari- 
ably appear in varying proportions, and, depending on the genotypic 
forms of the plant, some of these compact forms l)reed true while 
others segregate. 

In order to produce compact forms, it is not necessary that one of 
the parents should be a dense form. If the plant is carrving an inhib- 
iting factor besides the factor for density, it may appear lax although it 
has the potentiality of producing dense forms. Thus, Black Bearded 
Spelt, which has been used by the author, is perfectly lax, but when cross- 
ed with vulgare it produces lax spelts in the F,, and in the F„ an appre- 
ciable number of perfectly dense forms. The White Winter Spelt, on the 
other hand, produces no compact forms. The Black Bearded Spelt, then, 
carries a factor for compactness and also an inhibiting factor. Certain 



Squareheadedness and Density in Wheat 877 

forms of turgidum, durum, and even polonicuiu also have the abihty to 
produce dense types in the F„. 

The writer has had no experience with vulgare crosses which liave 
produced compact forms in the F, ; and unless the inhibiting factor is 
closely linked with the factors producing a certain specific form, it seems 
possible that certain vulgare forms will be met with which, although 
carrying the density factor, will be lax because of the presence of an 
inhibiting factor. 

The mode of inheritance of density in some species crosses is very 
complex, because new specific forms arise in such crosses, each of which 
is affected in a peculiar way by the density factor. Besides factors 
for inhibition, many inodiliers also may be involved. Often irregulari- 
lies are produced by the failure of development or maturation of some 
forms which seem to carry combinations of growth factors that restrict 
growth or cause various anomalies. Before being able to analyze from 
a factorial point of view the inheritance of density in such crosses, it is 
necessary to know in what proportions the various specific forms segre- 
gate. 

There are two cases which suggest that compact or semi-compact 
vulgare forms have been obtained through crossing two vulgare forms. 
De Vilmorin (1913) cites two instances in which lax forms produced 
dwarf forms. The dwarf plant, a photograph of which accompanies 
the text, appears to be a compact form much denser than the plant from 
which it mutated. It may also be possible that these cases were natural 
crosses with a com pactum pollen, since segregation of other characters 
occurred also. Another case is that mentioned by Neethling (1918), in 
which tall vulgare forms crossed among themselves yielded dwarf forms. 
The latter behaved as recessives. The statement is made that the dwarf 
plants had short ears, but nothing is said about density. If these were 
compactum forms, the fact that these dwarf forms appeared in a pro- 
portion somewhat less than 25 per cent tends to lend support to the 
possibility that the parent which carried the density factor carried also 
a factor inhibiting the production of dense forms. Until more is learn- 
ed about the behavior of the F. in the F,, no definite explanation can 
be given to account for its mode of inheritance. 



8/8 Sarkis Boshnakian 

In Plate LXVII (lower) are shown a number of dense forms of dif- 
ferent wheat species, most of these being synthetically produced in inter- 
specific crosses. Some show both compactness and squareheadedness; 
others show one of these characters in the absence of tlie other. Korn- 
icke (1885) has observed dense and squarehead varieties in other wheat 
species. He gives the following botanical varieties : Triticum durum 
Desf. var. compactum Ser., Tr. polonicum L. var. compactum Link., 
Tr. polonicum L. var. qiiadraium Ser., and Tr. turgidiim L. var. quad- 
ratum Ser. 

Density, or the excessive shortening of the rachis internodes, is not 
confined to the genus Triticum. Dense forms are common both in barley 
and in rye. 

The question of the origin of Tr. compactum becomes simplified 
if it is recalled that this form may be produced when a sativum form 
is crossed with another wheat species, and also that natural crossing 
occurs not infrequently. Such being the case, one would expect Tr. 
compactum to be practically as old a form as any of the other species, 
and, so far as archaeological evidences go, cultivation of Tr. compac- 
tum has been traced as far back as the Stone Age. Buschan (1895) 
states that this compact form has been found in the remains of caves and 
lake dwellings and among other prehistoric relics in regions extending 
from Egypt to central Europe and to Sweden. According to Unger 
(i860), the culture of wheat has been traced back to the year 3623 
B. C, and hence its origin must be older still. 

If interspecific crosses between vulgare and other forms are able to 
produce compact forms, it seems that the first origin of Tr. compactum 
should have followed that of Tr. vulgare. Undoubtedly Tr. compactum 
has reappeared many times in the same manner, for the appearance of 
this form in interspecific crosses is rather common. Tt'. compactum 
may be a mutational form of vulgare, although there is no dependable 
evidence regarding this possibility for vulgare wheats. There is a par- 
allel example in the case of the rye known as "Heinrich-Roggen" (Hill- 
mann, 1910:579). This is a very compact form of rye which is said 
to have appeared in 1880 as a mutation on a single ear. 



Squareheadedxess and Density in Wheat 879 

SUMMARY 

The density studies reported herein were made primarily on the prog- 
eny of a number of crosses in which the dense parent was Dale Gloria 
{Triticuiii com pactum), with an average internode length of about 1.41 
millimeters. 

Density was found to be dominant over laxness. The ratios obtained 
approached 3:1. The heterozygous forms were somewhat laxer than 
the homozygous dense forms, but by no means intermediate between the 
dense and the lax parents. The V„ curves were bi-modal and discontin- 
uous. 

The F3 plants showed various degrees of density within the dense and 
the lax classes. Proofs are given in the text showing that these varia- 
tions are hereditary and are the result of the segregation of modifiers 
or of additional density factors capable of producing density only with- 
in short ranges. 

Experimental evidence is cited suggesting that different density fac- 
tors form allelomorphic series, and other evidence that they belong to 
multiple series. 

Squareheadedness and density were found to represent two different 
characters. Hybrid progenies showed all types and grades of combina- 
tions between these two characters. 

The process of squareheading was found to shorten the average in- 
ternode length. The effect on density thus produced, however, is slight. 

The phenotypic transmission of the squareheadedness of Dale Gloria 
is dependent on the type of the lax non-squarehead parent. In some 
crosses there was a large proportion of lax squarehead forms in the ¥„, 
while in others there were none of these forms. 

Although in F„ progenies resulting from dense and lax crosses an 
almost perfect correlation exists between rachis length and density, 
these two characters are not necessarily correlated. Rachis length is- 
the indirect product of average internode length and number of inter- 
nodes. The correlation between density and rachis length becomes less 
and less as the difference between tJie numlier of internodes of the 
parental forms increases. 

High degrees of correlation were found between average internode 



88o Sarkis Boshnakian 

length and length of culm, length of sterile glumes, and length of ker- 
nels, and average rachilla internode length. These, together with other 
observations, show that density and the shortening of these other length 
characters are the result of a single dwarfing factor. 

Plants exhibiting the spelt character are not as much affected by the 
density factor as are those that show sativiiiii characters. 

Compact forms may be produced by crossing a lax sativum with lax 
forms of other species. Dense fonns may also appear occasionally in 
crosses where neither parent is a sativum. Compactness is not a char- 
acteristic of sativum forms; other species also may exhibit this charac- 
ter. 



Squareheadedness and Density in Wheat 88i 

LITERATURE CITED 

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BiFFEN, R. H. Mendel's laws of inheritance and w heat breeding. Jotirn. 
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Boshnakian, S. The comparative efficiency of indexes of density, and 
a new coefficient for measuring scjuareheadedness in wheat. Anier. 
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Buschan, Georg. Triticum. In Vorgeschichtliche Botanik der Cultur- 
imd Xutzpflanzen der alten \Ve\t auf Grand prahistorischer 
Funde, p. 1-34. 1895. 

Edler, W. Die Aehrenform des Squarehead in ihrer Beziehung zur 
Ertragsfahigkeit verschiedener Zuchten. Illus. landw. Ztg. (Cited in 
Die deutsche landwirtschaftliche Pflanzenzucht [Hillmann].) 1903. 

Hillmann, Paul (Editor). Die deutsche landwirtschaftliche Pflanzen- 
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KoRNiCKE, FriEdr. Der Weizen. /;; Die Arten und Yarietaten des 
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Leighty, Clyde E., and Boshnakian, Sarkis. Genetic behavior of 
the spelt form in crosses between Triticum spelfa and Triticum sati- 
vum. Journ. agr. research 22 1335-364. 1921. 

Mall, W. Die Ergebnisse verschiedener Getreidebastardierungen. 
Deut. landw. Presse 39:164. 1912. 

Meyer, Karl. Uber den Einfluss verschieden hohen Wassergehalts des 
Bodens in den einzelnen Vegetationsstadien bei verschiedener N- 
Diingung auf die Entwicklung des Gottinger begrannten Square- 
head- Winterweizens. Journ. Landw. 57:351-384. 1909. 

Neethling. J. H. A preliminary note on dwarfs appearing in Gluyas 
Earlv (wheat) hybrids. South African journ. sci. 14:540-547. 
1918. 

Nilsson-Ehle, H. Kreuzungsuntersuchungen an Hafer und Weizen. 
II. Lunds Univ. Arsskr. 2: 7*': 1-84. 1911. 

Ohlmer, W. tjber den Einfluss der Diingung und der Bodenfeuchtig- 
keit bei gleichem Standraum auf die Anlage und Ausbildung der 
Aehre und die Ausbildung der Kolbenform beim Gottinger begrann- 
ten Squarehead-Wintervveizen. Journ. Landw. 56:153-171. 1908. 

Parker, W. H. Lax and dense-eared wheats. Journ. agr. sci. 6:371- 
386. 1914. 



882 Sarkis Boshnakian 

I'reul, Franz. Untersuchungen iiber den Einfluss verschieden hohen 
Wassergehaltes des Bodens in den einzelnen. Vegetationsstadien bei 
verschiedenem Bodenreichtum auf die Entwickelung der Sonimer- 
vveizenpflanze. Journ. Landw. 56:229-271. 1908. 

RiMPAU, W. Kreuzungsprodukte landwirtschaftlicher Kulturpflanzen. 
Landw. Jahrb. 20 :335-369. 1891. 

RuEMKER, K. VON. Methoden der Pflanzenziichtung in e.xperimenteller 
Priifung. Landw. Inst. Breslau. Mitteil. 5:1-322. 1909. 

Sapehin, a., and others. Analyse hybridologique des caracteres cor- 
relatives chez le froment. L (In Russian. Summary in French.) 
Imp. Agr. Inst. Southern Russia 86- : 455-544. 1916. 

Spillman, W. J. Quantitative studies on the transmission of parental 
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Colleges and Experiment Stations. U. S. Dept. Agr., Office Exp. 
Sta. Bui. 115:88-98. 1902. 

StrampEli,!, NazarEno. Alia ricerca e creazione di nuove varieta di 
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1907:74. 1907. 

TscherjN[ak, E. \'0N. Bastardierung. In Die Ziichtung der landwirt- 
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Unger, F. Botanische Streifziige auf dem Gebiete der Culturgeschich- 
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ViLMORiN, PhillippE de. Sur une race de ble nain infixable. Journ. 
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Memoir 46. A Classification of the Cultivated Varieties of Barley, the eeventh preceding number in this aeries 
of publications, was mailed on March 16, 1922. 

Memoir 47. Typha Insects: Their Ecological Relationships, waa mailed on Dereniber 30, 1921. 
Memoir 48, The Inheritance of Salmon Silk Color in Maize, was mailed 00 January 30. 1922. 
Memoir 49. The Biology of Ephydra subopaca I.oeiv, waa mailed on February 16. 1922. 



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